I know unit animation isn't in the cards, and would minimize the whole board game aesthetic, but it would be nice if instead of sliding around the board they would hop like you would do in an actual board game. At least at lower playback speeds; I'm not sure how that would look at 8X. When they attack, they could tilt forward and sort of "slap" the unit they're attacking. Ranged dudes could lean away from their target and snap forward suddenly as their projectile is released. When a dude takes damage, it cold vibrate briefly.
I can't think of a game that does this exactly as an example, but I think my imagination might have been somewhat inspired by the movement of the characters in Stacking. If you're not familiar with this Double Fine masterpiece, it's a game where you control a tiny Matryoshka doll that can control other dolls by hopping into them. The way they animate these otherwise inanimate objects is really quite brilliant and charming. Not that it can be entirely duplicated here, but it might serve as inspiration for more or less what I'm talking about, which is hard to put into words.