Tommy gun and enough ammo = Marsh Hopper Mayhem
Just as an aside, if the developers really wanted to force a strict means of finishing that fight, they could patch out the ledge. Same goes for a few other sections of the game as well.
I mean, you can take a Were-bull charge while jumping to get boosted out of bounds and/or on the wall during some of the wave fights. It's all part of the game without outside interference needed to accomplish it, so calling it cheating or looking down on it in a similar manner seems like an overly judgmental view to take.
Besides all that, it's Serious f***ing Sam, not tournament sanctioned Dota 2 or some stuffed shirt rule laden game. When the core mechanic consists largely of backing away from imminent danger to remain alive to continue enjoying the game, finding a means to take even a slight breather from that shouldn't be considered a problem.