Well, the mystery deepens!
I went to the shop and saw the work being done first hand. The sock filter looked ok, and when air was blown through the hose backwards from where it connects to the fuel pump it flowed through. There was a little tiny (1" x 3/8") plastic coffee strainer looking thing inside the hose that looked clearly past its prime. That was removed, and the fuel strainer will be bypassed while an external FRAM filter will be placed before the pump. There is some debris in the tank, but nothing major. That will be flushed out and the tank cleaned.
Not sure if any of those things is the cause of the problem as the car started up fine for the shop after the tow truck dropped the car off. They drove it a bit and noticed the same hesitation at 3k that I get, but the car did not shut off. Maybe having the car towed caused the fuel to slosh around enough to loosen whatever is impeding the flow???
I don't know. This little car is kicking my butt at every turn.