Moment of truth!
Caps were around 14v. Turned the key, car started right up. Caps dropped to around 8.5v under load then bounced up to around 9.5v with a single start though, so they're literally good for just one start. Good enough if I pair them with some other battery that will top them back off, but I think if I were to recommend this project to anyone else, it would be with caps of at least 800F.