Not enough info is provided:
Pro’s lean over further in crit corners (are you a pro or local Cat 5?) ; how do you arrive at 57mm trail etc.
These kinds of questions are where the judgement of an experienced framebuilder is beneficial. I’m not saying I have that judgement (yet?) but, I’m realizing it’s important which is probably one of the intermediary steps to acquiring it.
57mm is common road racing bike trail measurement with roughly 73* HT and 43mm offset fork. It would be described as ‘neutral’ (ie not quick and not slow). This would make sense for a fixed gear bike on the road which has rougher pavement than a velodrome. For true crit racing, you may want to go a little steeper and less rake/offset but result in slightly more trail. I’m guessing there are off the shelf fixed gear crit bikes or track bikes you can use to make this call. Also, this isn’t the biggest problem to solve. You won’t win races on a bike with 59mm of trail that you wouldn’t have won with 56mm. Within a reasonable range, it’s almost irrelevant. It might feel different but that doesn’t make you faster.
BB height is your more important issue. I would bias toward a higher BB. The downside of a little higher BB is negligible - again, you won’t win races with a 5mm lower BB - but the downside of a pedal strike in a crit is catastrophic (for you and your fellow competitors). MTB SPD pedals will gain you clearance vs road pedals and at the highest levels, shorter cranks are all the rage.
That was my first thought - a fixed crit bike with 172s? I know even less about racing crits than I do about geometry, but I know pedal strikes are bad.
As for your design, start with what other manufacturers use - look at track bikes, crit bikes and tracklocross/fixie stuff. Specifically head and seat tube angles, BB drop/height, fork rake. Also look at bikes you (or your customer) already own or have ridden, what do you like or not like about them?
I agree. 75deg headtube, 370-380 a-c, 28mm offset. 74-75deg seat tube. Only concern here is toe overlap. If that’s an dealbreaker, consider sending the bb back a few mm via a bent seat tube. It’s worth it to keep that front end steep and tight, in my opinion.
I built my crit/fixed gear bike with 45mm of bottom bracket drop, which was admittedly too high. But I have 170mm cranks, and I have never pedal struck once!