There's another option as well, which would compliment a bayesian-style points/training system, and that's one of waiting until the end of a race, then looking at each lap time.
You then compare each racer's average lap time against the average for all racers, across the entire race. If we suspect them of cheating by being an order of magnitude faster than the average you could drop in a sanity check, by looking at their LFSW stats.
A racer with lots of races under the belt, and consistently fast times across all tracks, are less likely to cheat than newer players with fewer races. It also gives you a benchmark as to their prior performance.
It's a bit simplistic and it allows the cheaters to potentially cheat throughout the race, however at the end they could/will be banned for life/x days/whatever. You/we/I could probably do a nice mathematical model on it, based on how much you expect a racer to beat another racer, store that info, and so on. However I'm afraid that's a bit beyond my 'saturday brain', this morning.
The only large issue is the long standing problem of the subtle cheater, but tbh I'm not sure if a subtle cheater is someone you're ever going to be able to reliably catch.
Or the other option is that the server becomes more authoritive over the max acceleration, governs collisions, etc.