Alright, first of all, thank you so much @IchoTolot and @kaywhyn for the encouragement. That, along with just taking a bit of time away from everything, really helped.
@Armani, your solution to my R1 was definitely a backroute, but I incorporated a small part of it into V2's intended solution.

The tileset in question, by the way, is the tileset for the Medieval Tribe in
Lemmings Tribes, which, to avoid any confusion, is a
completely separate game from L2. Here's a wiki page about it that I put together a little while ago if you're interested:
https://lemmings.fandom.com/wiki/Lemmings_Tribes. Anyway, I was the one responsible for porting the tilesets over to NeoLemmix, and since its tilesets would fall into roughly the same category as the L2 and L3 ones (and since it doesn't have trap sound effects anyway), I just stuck with the default sound effects for traps, which is why the dragon (since it is a Medieval tileset I believe it is indeed supposed to be a dragon, but its design is quite dinosaur-like so you're entirely justified calling it a dino) sounds the way it does. Since these tilesets are directly ripped from an officially licensed Lemmings game, they should
probably be properly labeled and put below the L3 ones, but I didn't pay any attention to that or say anything on that matter when I uploaded them.

@Simon, your solution is, expectedly, another horrendous backroute. It's pretty likely I'll just throw out the Stacker entirely and adjust the level accordingly in V2. I had quite a clever use for the Stacker in mind when designing the level, but after some consideration I think it is
literally impossible to enforce without completely changing the spirit of the level.

There is indeed a reason the save requirement and exit cap are what they are.