Update, after kicking around our options, experimenting with driving the car around town with limited current, and speaking with the engineers who designed the 12Kw EV charger, the plan has transmogrified.
We need a lot of current for a good while, probably enough to make super caps impractical unless we pour tens of thousands of dollars into the battery box. Since we already have a huge crapload of Volt batteries laying around, we will probably be sticking with batteries.
The engineers for the programmable charger have assured me that it will survive this use case at our duty cycle if we get it enough clean air to keep it cool. This may require some kind of roof-mounted air ram scoop, but we wanted to do that anyway, just because racecar.
We were lugging the motor at CMP, which probably contributed to our overheating issue. After doing some experimenting, I have reassembled the shift linkage so we can use first and second gears again, and we will be using them going forward. This motor is happiest if you rev the hell out of it. The built-in fan also doesn't move much air, so I will be adding a manifold to one end of the motor and using some fans, probably Prius battery box fans, to move more cooling air through the motor.
All of this is still adding up to series hybrid, with the guts of a portable generator mounted where a passenger would normally be, a big-ass programmable charger mounted somewhere where we can get it a lot of air (roof?), and 25% more batteries, which will be managed using hacked Nissan Leaf BMS units.
It should be faster, have greatly extended range (hours?), and turn even more quiet hour laps than before, all without banks of generators running in the paddock or swapping out thousands of pounds of batteries.
I've been selling off generators, chargers, power supplies, and batteries. As of today, I had enough in the PayPal account to order the fancy charger, which should be enough for me to run a test configuration using one of our existing generators and battery packs to see if this idea will work at all. I should know something in 2-3 weeks.
Everybody grab your brooms, it's shenanigans!