Hmm okay. But there are separate keys for diagonal movement so you don't have to press multiple keys, so I don't really understand the issue completely.
I did notice that if I hold down a side key and press an up or down key quickly while moving, oftentimes it gets ignored. I don't like that and I can see how that's a problem if the character is quickly moving around the map and you want to quickly steer where he is going.
But that's if you are already moving. If you are just starting to move, I'd think people would deliberately select a key for whatever direction they are going. And everything happens immediately after you decide where to move, but I suppose that's the problem that needs to be solved.
So I guess the idea is to add a bit of time to accept more input before the character actually moves? Obviously, I can't have the player action change while the player is acting since it's turn-based. I'm not super familiar with this but reading
https://gamedev.stackexchange.com/questions/43708/fighting-game-and-input-buffer...
It seems 5-10 frames is natural for fighting games at least.