Water pressure regulator bad?
I've never heard anything as strange as trying to adjust your water pressure with a tap running, this makes no sense at all.

Turn your pump off, run the water until your pressure drops to about 30 psi, then flip on the pump again and see what pressure the pump stops at. if it's below 45 psi then turn the adjusting nut clockwise until the pump restarts and wait to see what pressure it stops at. If you want 60 psi then just continue adjusting until you reach the 60 psi you're after and that's it. If it won't go up to 60 psi then it could be the regulator isn't designed to go this high and you need the proper one to get the pressure you're after.