I'm thinking there is something to do with the rest of steering system being new and the pump being the OE one with 160k miles on it.
I hope that too!
I might give that a shot if it doesn't quiet down soon. Does anyone think this could be damaging to the new steering rack?
Duh line replacement, not pump.. you could very well be right. Couldn't tell you from experience because I had to replace my pump before my lines because it became unbearably loud as the weather got colder.
If you had the wheels off the ground and went through the procedure you've already outlined I wouldn't imagine there could be air in the system, and wouldn't think it would wear on your rack.. but then again, i suppose I wouldn't have expected it to whine either.
I know you shouldn't crank into the bump stops but I usually go slightly further at the stops until I hear it make the slightly groan just to be sure I've completely hit the ends and gotten out any trapped air.. found that the slower I turned the wheel the better it worked..
Usually let it idle for a minute halfway through after about 15 turns, just to let the fluid calm down a but and keep it from further trapping air.. then I'll take the last 10ish slower..
I'm sure this is the way you're already going about it, but I'm sure it wont hurt to keep trying to purge out air even if there's none in the system..
Keep us updated if the whine cures up