Like dogmush, I would have expected burnt fluid, but yea, unknown history with regards to the previous owner.
I don't know a lot about the 4R70W, but I rebuilt an E4OD/4R100 by myself, ripped down to nearly individual bits. From that experience, my approach would be to drop the pan and take the valve bodies off. Carefully inspect the spool valves for debris or damage. If that looks good, put it back together, hook into the pressure port with a gauge and check pressures in each position. That would break this problem down into "Am I dropping this trans or not?"
DIY rebuild isn't hard, but it isn't fun. Tedious. You have to be very meticulous if it's going to go okay. I had to make a couple tools as well. Pending the above tests, in your case, I'd consider swapping in a scrapyard transmission. Look for something with lowish miles that was in an accident. If it was in an accident, at least it was running before it came to the scrapyard!