I'm experiencing hard cold starts.

Is the fuel pressure supposed to drop while cranking? If not, what causes this?

The Fuel pump primes to about 38 psi, and holds, but drops to 10ish psi when cranking. It seems to do it in relation to the drop in battery voltage. When the car starts, it jumps up to 40-42psi and holds.

 

You're on it - Fuel pressure is affected by pump voltage. Is the battery voltage dropping below 10V during cranking? Regardless, 10 PSI seems extremely low. I would be wondering about circuit resistance including connectors, relay contacts, and grounds.