I have noticed that one effect of changing the geometry to four directional movement is that you need to skip turns. In eight-directional geometry you can just move to a side. Don't know why, but this was very noticeable to me once I added four-directional mode to Hydra Slayer.
Regarding the "when you and a monster have exactly one space in between you, you should not spend your turn moving closer to him" rule: I think a better solution would be to have monsters which also do exactly that...
If we want to have "no skip turn" as a design decision, then using skills and doing other actions should involve a movement too, IMO. Probably a non-movement action would take no time, but you cannot do that twice in a row without moving. Equivalently, you can either do a move or an action + move. You could probably somehow motivate why character can never stop.
