Texas, the edge tires should give you all you need for traction, and your setup doesn't sound too far off. Let me ask you: what kind of steering setup and servo do you have?
I've been racing 10T's for over 10 yrs. or so and have recently gotten into the GT's. outside of being heavier, there are many issues that are the same.
The pressure on those front wheels is a lot more than you think, especially when hitting a large turn at high speeds. One of the first things that was pointed out to me by a track owner was that he watched my 10T go into a turn and could visibly see the tires straightening back out. This meant that a) my servo was too weak or b) my servo saver was giving up some steering.
Bottom line, I put a Futaba S9404 (number might not be right!) servo up front, 111 oz/in torque and .11 sec speed, all metal gears and BB's. I tightened down the servo saver and the problem went away, I actually began getting oversteer and had to dial a little out with the D/R on the TX.
The same would be true if you're using the MIP maintenance-free steering with one of those servo savers that go on the servo; you never know WHEN those are giving up steering. I always rip them out and put the stock ones back in, the stock steering is smooth enough.
The only other thing: do you have holes drilled on the inside of your rims? Squeeze your tires. If they feel like they have air in them, drill a 1/16" hole on the inside of your rim so the tires are soft and squishy. You should hear the air whoosh out when you squeeze them.
Make sure your wheels are holding position before you worry about your setup!