why would you not go shorter cranks for a climbing bike?

shorter cranks allow for the leg to stay more extended at the top of the stroke, opening the hip angle. you lose short-term torque for a better endurance position. see TT riding and short cranks. I'd also build it with a single chainring. Save weight on the front derailleur and front brifter and just get a decent range in the back. like a 42 / 11/32 setup. something like that.

And I wouldn't skimp on tires. you're unlikely to lose a race by a handful of seconds, and you seem to have terrible luck with flats.