First, I got both characters into the red and yellow teleporters, but didn't collect any of the coins and instead got Loof's chompers to block Stinky's chompers (in the official solution, this happens as well but with Stinky's chompers blocking Loof's).
Following that, I kept Loof where he was and used Stinky to get the coins at the end of both teleporters, as his chompers would not be able to move due to the yellow ones blocking them. Following this, I completely skipped the boulder and steel box bit and put Stinky on the right side of the screen past the conveyors (similar to the walkthrough too).
I then navigated Loof over to the left side without the yellow chompers getting him, and as they can't go past conveyors, could no longer get him at all. Opening up the blue and green gates with both characters, I got the coins and then proceeded to get the bonus coins that were on Stinky's side, as the yellow chomper was stuck against the wall as it only goes after Loof. I kept Stinky by the exit and then repeated the same thing with Loof on the other side of the screen that has the red chomper.
With both of them by the exits, I finished the level without killing any chompers!
While it wasn't completed the way the official walkthrough says it should, I think it shows how some of the puzzles in the Wonderland games are well made enough that you can do them just a bit differently and still manage to beat the level, which is probably part of why there is so much replay value to these games, alongside the online custom levels, the level editor and the fact that they're just incredibly charming and fun to play.
