The original games too have the same problem of not having any fodder units to be creative or risky with.
I think introducing something like CO powers / super powers from advance wars would be a neat solution to the stalemate problem. Unlike regular skills, any of your units can charge your CO power gauge. You also get bonus charge if one of your units die (but not for killing, so that the receiving side can maintain some momentum). It could even make players choose between killing units or spreading damage depending on the situation.
We could also go days of ruin -esque and give bonus charge if the leader unit kills an enemy unit. Also days of ruin -esque, we could limit the activating CO power / super power action to the leader unit so that you won't have access to the super power anymore if they die. This can give more depth and strategic priority targets, and also somewhat solves the issue of not having any fodder units to be willing to initiate with.
Possible leader skills / super powers I'm thinking of are like +1 movement to all units, +6 to all ally mounted unit stats (or flyers, etc.), lead unit gets extra action, all enemy units lose 20% hp and allies recover 20% hp, etc.
:e and if there's still stalemates, make it so it charges by one every 3 turns or something