EDIT: Okay, I was able to completely skip the puzzle with the help of the asbestos vest, and a firebomb aimed at the ground, so I was able to boost myself into the exit without having to go through all the columns-pushing or dealing with every Enforcer.

Short version:
The only character you can finish Extreme ROTT with is Thi Barret (without cheating, anyhow).

Long version:
Okay, so I made it all the way to E4A2 in Extreme ROTT when I was having problems with a puzzle. I had everything figured out but my character kept getting stuck in a sequence where you have to hop from pillar to pillar. Scouring the Internet for an answer, I found this:
http://bd.baldurk.org/2126#title
Which pretty much revealed that you can't complete the level, and thus the game, with any character except Thi Barret (I was using Taradino). So if you're planning to play through Extreme ROTT legitly, use Thi Barret.