Well it seems to me that the battery/starter/charging system are meant to make the car "go" which is 50% of your goals. I would suggest getting one such as one of these:
Lightweight High Performance, One-Wire Alternators & Accessories and under drive it as much as possible such as off an axle so it is only working at speed. For starting I'd get a "starter cart" like I used to see a lot of vintage race cars have with a pair of huge batteries and one of those nice plugs to run power in the pits. If used with a small battery that can get you started in case of a spin and engine stall it will solve your issues.
Several years ago Ron Mistak in the famous number 22 Wayne Baker 914 IMSA was at a vintage race, got the car started okay but stalled it when pulling out of the pits and the battery was too small and pretty much dead and he could not get it running until several laps into the race. Remember to win you first have to get started and that requires some power.