White seems to have a pretty big advantage. Do you think maybe a simple rule of "can not move your piece back to the same spot on the next move - you have to at least wait 1 move before moving the same piece back to the same spot" would help?

And that is you can not move B3 to B4, then on your very next move you can not move B4 to B3. You can move B1 to B3, or move B4 somewhere else - but not back to the same spot.

Any other ideas?