In Mayhem 2 you can build through the gray part of the cannon that shoots the flamethrower because the cannon sprite is too big, while the old version is small. This makes "Feel the heat" too easy because you can just use all four builders at the beginning to get all the Lemmings out and they will fall through the gray part of the cannon. This makes me think the PSP was rushed.
Edit:
Looks like Taxing 3 is possible in the PSP but requires a different strategy, and I don't really know how to make the Lemmings turn around by having two builders close to each other in this version. It could happen when I'm playing "I have a cunning plan" with a lot of Lemmings building close together.
Step 1: Make the first Lemming build to the exit
Step 2: Make the second Lemming bash the stair leading to the exit to create a ceiling then make him turn around by making him build and do the same with the other Lemmings, to prevent having two or more building to the exit. In the picture I ended up having two Lemmings building to the exit anyway but still beat the level.
Step 3: Make the second and third Lemmings build a stair wall and have the fourth one build to the terrain that's on the left side. When the Lemming that is building to the exit is close to home, bash through the stair wall.