Something around this might be a starting point to summarize the battle rules: to win, a player's attacking letter requires two things. (1) All of the attacker's touching words to be valid; (2) At least one attacking word to be 2 letters longer than one of the defender's valid words. (But I don't this is all of it. It probably needs revision.)
Aside: I'm not sure what the _minimum_ level of complexity for the rules _could_ be. I get the impression these rules were chosen to make the game more interesting. Having known some game-creators, it is common for game rules to be play tested. But there is always the question of "play tested for what audience?"
P.S. I like the game so far. A lot. I see a lot of potential in it, but yeah, it is significantly more complex than Scrabble.
Aside: For instance, +1 is the defender's advantage in Risk, and I always loved the mechanics added by the Lord of the Rings version (and maybe other versions) where you could modify that advantage to anything from +0 (with a "leader" in the attacking army), to +3 (with a leader in a defending army on a tile with a "stronghold"). This is a bit different because it isn't dice rolls, but a similar idea.