First off when it comes to tires it's impossible for me to make a suggestion without knowing the track. I can give some advice tho; You need to chat up the guys who you say are "riding on rails" and find out wat they are putting on the rear wheels. Also if you're pushing in corners find out a tire that works good on the front. Based on your setup it seems you've already figured out you shouldn't be running the same tires and ompound from and back.
The first setup suggestion I would make is take those dual stage pistons out of the rear shocks and put in some regular pistons, this may require a change in oil as well. Problem with the dual stage pistons is they allow too much rebound, when weight shifts to the rear those pistons allow the shocks to rebound too easily and shift that weight back to the front. This hurts your rear traction, I ran those pistons all the way around for a while and I just recently took them out of the back shocks due to this reason. I have left them in the front because my track and basing surfaces are very uneven and require my front wheels to absorb a lot of minor bumps and still keep the tires on the ground and I have no problems cornering so I don't think it's hurting me there.
Also another basic way to reduce spin outs is to either increase the punch ontrol setting in the Esc or loosening the slipper clutch. I race on a very dry, dusty low grip track and I have to run a very loose slipper to help me out when I grab too much throttle out of a corner.
One bit you left out that's pretty important, what are your camber angles all around and what's your toe upfront?
Electrix Ruckus EzRun 60amp esc + Vxl motor
Axial SCX10 Sidewinder Sv2 + Tacon 1200kv motor