Nothing wrong with the bmw diff, just not lsd. Caterham’s tend to spin a rear wheel on slow exits so an lsd is a fix but not allowed in many race series.
Academy lap record Is 1:54 on Donny gp, it’s 1:40 for a 420r (Duratech) so it is much slower. ECU change and you can make a Sigma a 310r which is about 1:45.
Tbh, I’m not good enough to bother with more power.