Racing on twitch with Beyond Chaos

I like the idea of limiting the number of fights we could run from, as part of a race to reach the 3 switch room. Unfortunately, I'm not sure exactly how we could efficiently limit the number of fights we could run from. Sure, we could say, we can run from 0 battles, but there are times I've legitimately run from battles out of danger, not out of speedrunning. Additionally, sometimes there are encounters that are basically impossible for the area they can show up in, though that might have been phased out by this version. I remember in one of my first runs, there was an enemy with 30k-ish HP, Atomic Ray, and 800 damage physicals outside of Kohlingen in the WoB. If something like that were to come up in a no running race, we'd just have to pick a god and pray that we never see it at all.

On the other hand, limiting number of escapes to x might be difficult as well, because there's no way I'm going to be able to keep track of that AND the dungeon layout all at once without some paper or something.

I really have no suggestions as to what the ideal option should be, I just figured I'd point out the possible obstacles with the methods I could think of.