So i am late to the party, but here my two cents. well. two hundred really.
I was going through that thought process myself when i redeveloped my personal hero quest. Here is the essence of what i found out:
Movement dice* Movement dice had their disadvantages, as moving 2 spaces or 12 spaces is just crazy different. So i was removing them.
* Removing movement dice was not good. Everything became much too calculable, so it was getting boring, fast. I re-instated the movement dice.
Minimum movement* Instead i made a new equipment that avoided frustration a little bit: Good shoes allow you to move at least 4 spaces.
* In the context of the heroquest board, where there are very few rooms with more than 5 spaces depth, this is more than enough. Those shoes are also a good gold-sink and can be taken away from time to time, for sinking even more gold.
* I made custom rooms for end fights, which are bigger. They are also bigger than the usual center room. Here, people were really happy to have the shoes.
Maximum movement: Run* There are missions where you traverse the long side of the board once or twice, a few badly designed quests make you even traverse it even three or four times. With average dice results, traversing the board costs three turns and is quickly done. However there was ALWAYS one character that was rolling less good than the others. So i invented "Run" as an action, that allows to add 3 movement to your roll, on the cost of your action.
* I experimented with 2 added movement: It wasn't used.
* I experimented with 4 added movement: That was a speed up that was crazy.
So for the Heroquest board size, 3 added movement were perfect.
Different boardsI mentioned the board size several times. I experimented with:
* The Heroquest Board
* Conan game boards
* Zombicide black plague game boards
* Space Crusade game boards (with space crusade models of course)
* Enlarged Heroquest Boards (not more spaces, just bigger spaces)
* A cut-down enlarged Heroquest Board to be used as modular tiles
The result: The movement rules and all range rules are highly dependent on the board you use. No surprise here. I share some details.
The number of squaresThe original heroquest board is traversed in three turns usually. If you use the same movement rules on the space crusade game board (2x2 tiles, 24 spaces), you traverse it in four turns, which actually feels a lot longer and takes between 10 and 20 minutes more real game time. That finding surprised me - i came to the conclusion that i wouldn't want games that regularly take more than four turns to cross the entire board. An exceptional mission is different of course.
I adapted the movement rules to cross conan game boards in three to four turns (you move 1 or 2 fields then - still thinking about a dice rule); and for zombicide the same game, i adapted so you would move 2 or 3 fields on a zombicide game table (also still thinking about a dicing rule). (i use 2x3 or 3x3 zombicide tiles then).
If you play on a geas game board with 54 squares, i would advise either for an average movement range of 15 squares, or have shorter movement and use only a quarter to half of the game board in most of the games. Even in the much smaller Heroquest, many quests use only half a board.
board field sizeThere are obvious differences between conan/zombicide like spaces which are designed to take a lot of models, and heroquest sized spaces which are principally there for one model only.
Less obvious is this:
When i bought an enlarged Heroquest game board with 30mm spaces i did this to avoid the overcrowding of the old 22mm spaced original board.
Now the models are physically more apart from each other, and changes become really obvious when we discuss diagonal line of sights. The 22mm board was a pain in the ass in crowded rooms. It was so crowded it was obvious that you couldn't shoot diagonally, for example, and if only one field was occupied even models with special abilities hat to take the corner.
Not so on the 30mm board. We applied the same rules first, but the little bit of spacing extra changes everything, visually. Now, if you go down to model's level, you can clearly see between two diagonal models, no problem. Also for diagonal movement, if only one of the two spaces is occupied, normally it is not fully occupied anymore. So diagonal movement looks like it is possible if one square is occupied.
In the end, we decided against changing the rules for the new board, but this experience showed that there is clearly a high dependence of rules and board.
Now to your point:
Diagonal movementAs said earlier, those kinds of things are so dependent on your game board that we can give you advise about our personal tast but as long as no-one has seen your board with models, no-one can really give advise. Some few things can still be said:
* I experimented with giving everyone double movement. Then a straight movement would cost 2, and a diagonal movement would cost 3. That was based on the same line of thought like whitebeard's, cutting the corner is making 1.41 length of way. An alternative would have been to count 2, 1, 2, 1 when moving diagonally; which i didn't want as it was too complicated.
I tested this not on a Heroquest board but on Space Crusade. There, both sides have a group to play, and if you play it with the right set of rules, it can become quite tactical. So i was looking for something tactical in movement as well. This type of rule works very good. The range of a model in an open field becomes approximately a circle, much to my pleasure.
And, slippery slope argument: as you already have cut into the area of assigning a movement cost to each square, you can immediately proceed to assign different movement costs to different terrains; which is a great option. (I use that one now if i do overland questing: Each square has two numbers printed on. The one you pay when entering straight and the other you pay when entering diagonally.)
* We found the need to define if you can go diagonally through a monster or corner or not. It really was a need, it just felt much too weird sliding with half your model through a ceramite wall plating.
We did it simple: Any diagonal movement cannot be done if one of the two adjacent fields is occupied. Again for simplicity, we didn't distinguish between a adamantium-hardened dreadnought, wall plating or a mouse.
What felt great for Space Crusade, didn't feel all so well for Heroquest. We started doing it, just for finding out that we used it nearly nowhere, simply because of the board properties. Rooms are stuffed with furniture, hallways are one-square-wide, monsters block the way - after two games,
we decided to drop this rule for the Heroquest Board even if we liked it.
We keep the ability to go diagonal, but it is a special ability for some very dancy characters. They are allowed to move one field per turn diagonally for the orginal cost of one movement point. The speed up effect here
is part of the bonus, and the weird ability of going between two monsters or slipping around corners is accepted because it adds to the character's ninjalike/dancerlike description just nice.
Zombicide and Conan: It is absolutely out of question to go diagonal on a Conan Board. The irregular field shapes sometimes don't even allow to define diagonal.
In the case of Zombicide, the speed up effect would be so crass it would become comical. Also, there is rarely a space on the Zombicide board that does not have a corner at least on one of the two diagonal sides. So, for Conan and Zombicide, there just is no diagonal.
Again we have seen that it is highly dependent on the board.
Heroquest: Possible but not attractive due to the room layout, but makes for a nice character extra rule
Space Crusade: Really a good option, especially after the 41% longer range is taken into account for
Zombicide: no way
Conan: no way ever due to irregular field shapes
Now, I don't know your GEAS Board. If you have large open rooms with a lot of squares, it might be attractive, but i really would do something about the 41% boost. The 2 points straight/ 3 points diagonal rule we used works really great here.
If you have small rooms and aisles, just let it go, don't do it.
If you really want it and it is something to be done by everybody, just please care for the weirdness with something simple.
