However, the pump sure does whine a lot. Much louder than the old pump! It's dark now so I could be slightly low on the fluid but I think it's at least above the low mark. Am I just still a little low or is this thing going to be that loud??
I've heard a bazillion different ways to bleed the steering system. There's a PDF floating around here if you search for it.
This is what I've done on my hydroboost swaps and I've had good luck:
Leave the motor off to begin with.
Fill the system to the line on the filler cap. I leave the filler cap off and put a length of old heater hose on that has the right ID to fit onto my reservoir. You may have to just leave the cap loose and drape a rag over it -- fluid will spray everywhere if you don't.
Jack the front end up so the tires are off the ground.
Turn the steering wheel back and forth, say 10 cycles, then do another 10 cycles with your foot on the brake. This will bleed the hydrobooster as well as the steering box. Might check fluid level halfway through as it can go surprisingly low quickly. Don't push it right at the ends as that makes the pump work extra hard, be gentle when you're close to the stops. At least since the tires are off the ground it's easy enough to wiggle.
Once done, check fluid level one more time, then cap it, start the motor real quick, and do the back-n-forth again. Turn it off, check the fluid level, then turn motor on and do the brake + back-n-forth.
May be overkill

but works for me. As mentioned, once the pump gets aerated you gotta turn it off and wait what seems like forever for the fluid to un-foam and then start all over, so doing it in steps helps.
-- A