You're not alone, this is one of the reasons I got a variable power supply! Hopefully I can moderate the flexis down to our old reflexes, lol.
Garry, I think a variable power supply will suit your needs just fine. I occasionally run at a local hard body club that has a 4-lane Tunkel track powered by a variable supply set at about 10 volts. We don't use a flexi chassis, but run scratchbuilt jalopies & use brass FCR & H&R chassis in late model sportsmans. What you use for chassis is less important than what you use for motors. The jalopies & H&R late model sportsmans use the H&R Hawk, an 18,000 RPM motor. The FCR late model model sportsmans use the Parma Deathstar, a stock Chinese 16D. Both motors are very driveable on the reduced voltage. The older 36D & Pittman motors you mentioned ought to run good too. I have a couple of each, but don't currently have them in a car. Be sure to post some photos once you get your track set up.