Okay, I've TASed up to the first Labyrinth entry, and the first encounter seems to be set to trigger at a specific spot, regardless of what I do.
During the first encounter, though, is where you can manipulate the next encounter. The next encounter is determined at the end of a battle (by fleeing or by victory), seemingly based on the end frame. Waiting no frames and fleeing, 5/10 frames and fleeing, using a hammer and fleeing, and jumping and fleeing all result in another random encounter at a different number of steps away.
Also, moving diagonally advances the step counter faster than moving in the cardinal directions. This could be used if only a small number of steps is needed to get out of a dungeon, but you need to slow the step counter to avoid an encounter.
So, basically, I'm going to have to have a way to determine the ideal frame to leave a battle. Trial and error will be too painful a task to get this done. I've read up on luck manipulation in RPG's but it's a bit too far beyond my knowledge to figure out on my own. Any help is appreciated.
EDIT: At the start of the first battle I am ~25 seconds ahead of the SDA run. Around 8-10 seconds of this are due to the runner getting a Matchbox by answering Sanary's question; I plan to manipulate the Matchbox in an encounter with a Slime + Pumpkeeno in B2F (along with a Bottomless Cup) to get a level up before a Mystic Sword and create a Novice Drill.