I've been turning my 337 a lot lately and refining my method a bit. From what I've read most people solve by layer, but I've found it much faster to solve the 16 split pieces individually to make a 3x3x3 and then solve regularly. By using a messy top layer as a PLL working space and storing complete tricubies (if you can call them that) in the bottom layer, half the pieces can be solved quickly with top layer face turns. The remainder can be fixed with a setup slice move, PLL and reverse setup move. You can switch a complete piece to the bottom layer quickly with a (z --> T-perm) and no. 21 from this page to re-OLL your workspace. http://badmephisto.com/ollpage_print.php
I do all corners first, then permute individual edges, mostly because my U-perms are relatively quick, and there can be quite a few near the end of the solve if you do edges last, although by using three cycles you can protect some pieces within the working layer, and if you get lucky and have a good look ahead you can get some really smooth solves.
I'm almost down to 2 minutes, could ppl post some PBs and other views on methods for this puzzle if they're still fooling with it please? I'd kinda like to get this puzzle sub 60. It's one of my favourites.