Aaand... victory!
http://prntscr.com/lflt14@srid - since you asked, I recorded this run.
https://www.youtube.com/watch?v=Bf8xvIF2TZUAgain, the strategy here involves scumming for APHEELSIK and WEYTWUT. That is pretty aggressive scumming, and one of the reasons I picked Shadow Heart was because I really didn't want to have to scum for a favorable god combo (Jehora or Binlor -> Dracul) on top of those. I lucked out with getting both Whurrgarbl AND Venom Dagger, but if I'd gotten some high conversion value shop items instead I maybe could have hit 20 HP/tile regenerated.
The most room for improvement I have with this character is figuring out when to time his conversions.
As Nurator said, the Troll is at his strongest when fighting an enemy who deals as much damage as the Troll regenerates in 6 tiles. Since most VT bosses do 120 damage, that means you want 20 health per tile, which is not feasible. However, if you go up to 7 tiles (which is more efficient than hitting other enemies to give you extra tiles and only hitting a boss with your DP) you only need 17 HP per tile - I only figured this out towards the end of the run and kept APHEELSIK for half of the fight with Frank, where it was giving me no value whatsoever. I should also have converted Venom Dagger at this time; though it would not have helped me reach the regen threshold I mentioned earlier, it would have allowed me to squeeze out a couple of extra tiles from hitting enemies.
Also, I sometimes forgot to spend my health on low-level monsters before using my DP with the self-cannon, and in general am not very good at remembering to make the most use out of Troll Brain. With WEYTWUT especially, what you want to do is position the enemies you're hitting to shroud tiles close to the direction you are exploring in, so that you don't waste your shrouded tiles.
Aside from that, that's two big challenges that I've completed with the Troll, the other being Curious Naga City. I would say he's actually one of the best-designed classes in the game. Most of the other monster classes are either not particularly different from normal classes (Half-Dragon) or have severe handicaps that limit how you can play them (Rat, Vampire). Troll is a perfect middle ground because it HAS a handicap and has a very technical playstyle, but at the same time can be played in more ways than almost any other character while remaining "optimal". At the same time, there is no god that is obviously the best for Troll, the way there is for Gorgon and Rat (almost always Binlor). Aside from TT, Troll also doesn't have any gods that are completely useless to him the way Rat does. Troll's playstyle is simlar to Gorgon as he is also a regen fighter, but far more technical and without the same safety net that Death Gaze gives. So all in all, Troll is my new favorite class!