Don't run the drag radials on an autocross course. Drag radials, by design, have a weaker sidewall to allow for flex during hard launches. Autocrossing requires very stiff sidewalls to keep the tire from "rolling over". So, although the drag radials might not "peel" off, you will damage their sidewalls using them for auto-x.
In terms of 20" autocross tires, see my sig for what I'm running. Your best bet is to run as wide a tire as possible front and rear. I'm looking into running 10.5" or even 11" rims up front for my car.
R-compound tires are hard to come by in 20". In fact, I think only the Toyo R888s are 20" R-compound.
Vengeance Kaotik Cam, C.A.I., ARH LT, Pypes Cat Back, ZL1 Shifter+2012LS3VERT bushing, Quantum Brake Ducts, JDP Tow Hook Scorch Yellow Trim Kit, Shark Fin, AAC DRLs+ABLs+SMDs, ZTA Rear Spoiler, R.Y. 1LE Splitter. Pfadt coilovers, camber plates, trailing arms, Pegasus Solid Subframe. Pedders ZL1 barz, radius arm & steering rack bushings. BMR adjustable toe-rods. Hotchkis Max Chassis Brace. ZL1 GMPP Driveline Upgrade. TurnOne P/S pump.
447 HP @ 6180 RPM / 418 TQ @ 5100 RPM