So as Mecha pointed out all those years ago, you can indeed skip levels with the 'Game Over Glitch™'
Basically you get a letter of PLOK every time you complete a stage without dying. You can also find these letters as pickups in some stages. Using the current any% warps route, it happens to work out that you enter both Plok Town and Real Rumblings (tank stage in flea pit) with P L O, which sets you up perfectly for the game over warp. Simply get the Plok letter, get a continue, and game over. The game will spit you back out onto the map with the level completed. My theory is that whatever flag gets set when you obtain a letter from beating a stage without dying is also set when you simply obtain a letter pickup in a stage. Then all you have to do is 'exit' the stage, via game over. It is fastest (I think) to drain all your surplus lives on Sponge Rocks, as the logs at the beginning prove to be the closest damage source to Plok's spawn point in any given level.
You can see this in real time here:
https://www.youtube.com/watch?v=HDlHSNm7G2w#t=9m30s
https://www.youtube.com/watch?v=HDlHSNm7G2w#t=27m20s
I'm not sure if Partyboy or Kooz have any intentions of redoing their TASes any time soon, but this would certainly shave whole minutes off the run.