Good point that a game being "easy" doesn't necessarily mean it can't also be enjoyable. "Simple" also doesn't have to be "boring" (people pick the Barbarian instead of the Wizard not just because they think the former is strong and the latter weak, but because they like not having to manage an extra pile of cards with their character, while the opposite is true of other players). When I've played as Zargon going over these official quests, I've tended to add things too, rather than subtract. In video games I always liked when difficulty increases added more enemies (or enhanced the strength of existing ones) rather than just starting you with fewer lives or less ammo. So that's been my philosophy as well as a GM in HeroQuest trying to moderate difficulty.
In practice this means that over time I may have to add more challenges because old challenges are nerfed, and hard quests will be completed but they will take a LOT longer to play. Occasionally instilling fear in your confident heroes is a good thing, so long as they don't become frustrated and full of despair (they will rage quit, and the game will be over).
The easiest thing is that you could entirely skip the Game System and just start on the expansions, if the only thing holding your people back is the notion that the game is "too easy" because that's really only a criticism that hits the first campaign. Even the upcoming "First Light" (which nerfs several of the spells as well as some of the Equipment) upgrades the difficulty and complexity of its starting 10. Pretty much every other expansion out there assumes that you're experienced either in terms of playing the game, or having saved gear, and purposely gives you an increased challenge.

Please note, I don't necessarily think the following suggestions will make the game more fun for your group. You'll have to discover what it is that they like and lean into that. But if simple challenge is your goal, any one of these could up that for you, easily. You may want to warn your players that you've made modifications to make the game more challenging, and I would emphasize that they asked for this...

You don't want them to be bored, do you? Many of these rules can be dropped or changed before you take on the expansions, because those are harder and don't really need as much tweaking, probably.
If you want to make the Game System more challenging, even up to the point of making it unplayable, you have many options out there. Notice I didn't nerf any spells or make the crossbow less fun to use. I didn't suggest that cards should limit supply when it comes to Equipment, but those are things others have tried as well. I tried to focus on changes Zargon can make on the fly with very little homework required. After awhile your heroes may beg for mercy (unless they quit the game, yes, even adults can be sore losers, especially if they think the GM has rigged things against them purposely), so be warned. Even without "rocks fall, everyone dies" moments, Zargon may inadvertently lose his playing audience if he isn't careful.
1) Upgrade the monsters. Some clever suggestions have been made like allowing goblins to move, attack and move on the same turn, or skeletons attack diagonally (that's from the companion app), but you can go further. Give all the monsters an extra body point. That alone is a big deal. Or if you really want to make things difficult, let monsters defend on white shields (instead of black) that makes the fights much tougher. Or if you're Zargon and want to fine tune it, you can go through the maps and change stuff. Yes, you can tweak every aspect of a quest. But you can replace your goblins with orcs, your orcs with fimir (or Abominations as they're called in the modern remake edition)... replace skeletons with Zombies (you might run out) and zombies with mummies (and if you're really crazy, mummies with Chaos Warriors.. er "Dread Warriors" in the remake). Boom! Much more challenging.
2) Limit gold. Yes, you can make the gold rewards smaller. They may not like this but if simple challenge is your goal, making the wealth more scarce will holds the heroes back. You can also adopt the EU rule and make it so that each room can only be searched ONCE for treasure (as it is, each hero may search, and so the treasure deck is possible to be drained of good cards in each quest, while using this rule means only a portion will likely be found).
3) Limit carrying capacity. Some people suggest limiting each hero to two weapons and they have to wear all the armor they're carrying (not counting artifacts, or maybe counting artifacts if you really want to). If they have more, they have to sell them, trade them, or drop them!
4) Potions expire. Yes, in the EU edition if you didn't use a potion within a quest, you couldn't carry it to the next quest with you. Granted, you also couldn't BUY potions, but it's up to you whether you want to make those expire too, or simply not sell them between quests to begin with.
5) No shopping between quests. I don't like this idea because it takes away a really important and fun aspect of the game, but some have suggested that once the campaign gets going, you're not allowed to shop between quests. If this is the case of course, gold becomes useless. Well, the only purpose gold serves now is as "points" I guess, but at the end of the campaign you'll have big treasure pile to buy more gear for the next expansion, then do without for awhile, etc. No shopping would conflict with the "limited carrying capacity" thing unless you want people to be dropping a trail of gear as they go. Heroes will trade equipment to each other and then drop what they can't carry, traveling light and some pieces of equipment from the Armory won't be found or used until they get into the expansions.
6) Use the Evil Wizard Deck. Let Zargon do stuff when there are no monsters on the board with threat cards. Look it up on this site!
7) Boss dice. You want monsters to be really strong? (You could use these for named "boss" monsters, or any monster). These guys will have very strong attacks and hero-like defense. Every fight threatens to kill someone. Might be overkill, especially in combination with the others. These can be purchased from Etsy or you can make your own.
NONE of these tips are advisable for the extremely broken difficulty Barbarian Quest Pack: The Frozen Horror or Elf Quest Pack: Mage of the Mirror. These are so difficult, you need every bit of gold, shopping, and perk you can for your heroes. You will be hiring mercenaries whenever you can (and they will die like flies) and you'll be lucky to survive if Zargon doesn't pull his punches!
Actually, the difficulty of most of HeroQuest after the first 14 quests doesn't need much to make it challenging. Unless your heroes are overflowing with gold and potions, they will be fairly challenged everywhere else (especially the two I mentioned above, if anything, Zargon may wish to edit those quests to make them a bit easier! removing some of the monsters or downgrading them, removing some of the traps, adding more gold & potions, etc).
Finally, I think what Doug Hopkins said is pretty spot on... that is (other than Kellar's Keep and Return of the Witch Lord) the expansions actually play just fine if you have a beginning set of heroes, rather than one that has lots of gold, potions, artifacts and equipment already.
The exception once again is Frozen Horror and Mage of the Mirror. In theory these were designed for a "fully equipped" (in terms of the Game System) party of heroes, except one. The Elf or Barbarian in those is assumed to be a basic hero... and he or she plays the three solo quests to get equipped. The trouble is those quests are a little too difficult for such a basic hero especially played by a beginner. They're very frustrating and reliant upon luck (assuming Zargon isn't just handing them the victory or they're cheating somehow). These quests could be played with a group (2-3 years is fun, 4 is a bit easy if you make no other changes, though you'll probably want to give extra rewards for the extra players in that case... it's the opposite of trying to make it harder, these expansions are too hard, you're trying to make it easier!).
My group that has played Frozen Horror, to Mage of the Mirror, to Crypt of Perpetual Darkness, I'd say about partway through the Elf quests I thought they had mastered the challenges. They were so powerful (and I gave them many new perks, knowing what they were up against) that I actually started putting in more things to make it more challenging, not less! (I delved back into the old drafts of Mage of the Mirror, which had many more and more powerful monsters for example) and I used my Evil Wizard and Combat cards to the max (the final battle of MOTM for example took something like 3 hours!). From here on, I am either finding ways to part the heroes from their gold or getting them started with new characters for the other expansions. It's still fun. Of course the way we play, on stream, the audience can also buy things for the heroes (or for Zargon) so even if they were penniless and luckless, someone might become their advocate and help them out. Of course as the stream owner I have the ability to tweak how many (and how "expensive" In terms of channel points) those perks cost, so there's still some balance.
Other points:
Frozen Horror from 1992 and the modern edition are basically the same... Avalon Hill realized too late that people understood it was too hard, so they put out "Into the Northlands" a digital quest (the PDF has suggestions on how to make it easier and better... but keep in mind Zargon has to use his planning and discernment to implement these changes).
Mage of the Mirror remake edition is much easier than the 1992 original. Even so, you may still consider tweaking it (Zargon does homework) to make it easier, unless of course you are playing with a group that has saved up mountains of gold and potions (such a group will complete just about anything after awhile, unless they simply give up).
Before playing "Rise of the Dread Moon" or "Jungles of Delthrak" Zargon should STUDY UP on the new rules. He should know the Game System rules by heart, and he should read ahead for the quest about to be played. Read through the Quest book (at least up to and including the quest you're about to play), study the new hero mechanics and the new cards. This is something I can't stress enough. Without it, you'll be debating with yourself how to handle new situations that arise, and wasting time flipping back and forth in the booklet reading things over and moving your cards around. These expansions are clearly much more advanced and complex than previous expansions (especially Rise of the Dread Moon) and they contain optional rules as well, meaning Zargon has to make a choice and can't just simply play as written. The players may feel casual, but Zargon has to be on his toes for these.
The key I think is teaching your players that HeroQuest is very easy to mod and there are many ways to play it, so if they don't like one way, that doesn't mean it has to go on the shelf and disband the party. Good luck!
