It still sounds like the fluid isnt flowing how it should...only possibilities I can think of are
1)Bad P/S pump: You said it whines sometimes, which is a symptom of fluid starvation...which can cause pumps to go out...
2)The reservoir screen is still dirty: I know you said you cleaned the tank, only reason I mention it is because you didn't say what you did exactly. You have to get a couple cans of brake cleaner (that's how much it takes) and spray it in there from every angle and drain it out again and again, as you scrub the screen with a toothbrush or something. Obviously the walls of the reservoir shouldn't be dirty but the screen is really the focus of the whole operation - if it's clogged then fluid can't get through as well as it should. Alternatively you could just take out the screen and put in a Magnefine P/S filter instead.
I also don't know how you went about bleeding, or flushing the system. But the best way is to take off the return line and route it into some kind of large container like a gallon milk jug (you'll need some plastic tubing to do this). Fill the reservoir, then have someone else start the car and start turning the steering wheel slowly in both directions, all the way to full lock, as you pour fresh fluid into the reservoir. It should suck up the fluid FAST (like almost faster than you can pour), if this doesn't happen the pump is probably gone or there's still some kind of restriction. Also this process takes at least 3 quarts.
Can't think of anything else, except...you are putting in automatic transmission fluid, and not power steering fluid, right?
