The sorex 36R is NOT a carpet tire. I've never had good luck with these. I run on a highly abrasive indoor asphalt track that is hard on tires, so we run sorex 36R's so they actually hold up through a run. The track also has very very high traction. Personally I prefer sorex 28R's on carpet.
So it sounds like most of your problems are coming from an improper tire for the track surface. If you have to use the sorex 32R's, then try and just soften up the car a bit. Angling the camber links (fewer shims on the inner pivots) will create more mechanical grip overall. Maybe even ad a little more rear toe in.
I'm not 100% sure on the TC shock towers having the same positions as the WCE. I do know that the TC shock towers are thicker, and they are slightly lower to accommodate the taller upper bulkheads.
-Korey