Having just replaced my PS pump, I sympathize with you. There's a seal on the pump, that if loose, could theoretically let engine oil into the pump. My pump would completely drain out in 3 days just sitting, even with all hoses replaced.
There are two rubber seals (o rings) internally behind two of the hose fittings that you can't see, and in my case the PS fluid would drain out.
I doubt that its engine oil displacing PS fluid, but it does sound like pump is out.
The chain remans ( NAPA, O'reilly, et. al.) are junk. I went through 2 NAPAS, until I found a local shop that specializes in Power steering pump rebuilds ($68). Maybe they ship (Raven Power Steering Specialists, Denver, CO, 303-777-6640).
The stealer wanted $720 for a factory new one, and the mopar4less wanted $450. Rockauto is cheap remans too, so if you've got a local shop like Raven, I recommend the 2 man shops that still care about their work.
97 2500 4wd, AT, 3.54, 550k +, stock except for AFE filter and BD steering brace.