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.
C.A.I., Apex Scoop, ARH LT, Pypes Cat Back, Barton Short Throw, JDP Tow Hook
Scorch Yellow Trim Kit, Shark Fin, AAC DRLs+ABLs+SMDs, ZTA Rear Spoiler
Pfadt coilovers, camber plates, trailing arms & differential bushings.
BMR adjustable toe-rods. Pedders ZL1 barz, rear cradle inserts, radius arm & steering rack bushings.
Hotchkis Max Chassis Brace (minus tunnel cross-over piece for SCCA rules)
1LE 3.91 gearzzz. Drive Shaft Shop Road Race Axle Upgrade. TurnOne power steering pump.
Forgeline GA3-R 19x11 + Hoosier R6 315/30R19
426 HP @ 5550 RPM / 427 TQ @ 4700 RPM