I just went out to the garage and tried again, this time with a quieter (cordless) drill. I took a quick vid with my phone (forgive the awful quality; it's dark here and my phone battery was too low to use the flash). Guage is a dash-mounted gauge on the end of a long capillary tube just propped-up inside the windshield...
With the quieter drill, I can now say the oil pump doesn't make any unusual noises... it just doesn't turn smoothly and there's a lot of vibration felt through the drill when priming it. Pressure rises quickly to 65psi however (I think it would've gone to 70, which the pressure relief spring is rated for, but my drill battery needs charging).
What do you think? Normal?
I also found this vid and this guy's oil pump sounds similar to mine (pretty noisy)...
Hard to tell though.