That's what I ended up doing. But, from my perspective - the issue is that you cannot win if she attacks you base. Fullstop, she moves first before your units, and uses an attack that removes all units in a row/column as long as they don't have flying. Plus, her winning by default doesn't count as a game over. Instead, She attacks your base again immediately, because your units still exist. Thus, you get stuck in a loop where she attacks, moves, slashes, wins. While your units take a small amount of damage each time, until she finally kills them. If her attacking your base is meant to be an instant game over, then it should just be that without fighting her. If you are meant to be able to fight back, you should actually be able to do that. None of this - game over after 10+ battles from her before your week starts.
As for using flying to counter her, do any of your units start out with flying? Unless there's a heroine that does, don't all the units with flying need to take an action first to start flying? I.E. you can't do that because she moves first and ejects your non-flyers?