Yes, I did a drain & fill at 98K (18,000 miles ago), and the fluid that drained out of drain hole at the bottom of the pan was very clean, and sediment free. What I'm seeing now coming out of the fill hole is brown, thin, and frothy, but still clean. So I just drained a little from the drain hole, and it looks like very clean ATF - no trace of coolant in it, which argues against the coolant-in-the-trans theory, since coolant is heavier than ATF, and should settle on the bottom. But the fact that there's so much of this brown frothy liquid coming out of the drain hole is very strange, although I agree that I'm not going to assume a compromised AT heat exchanger is the problem without further investigation. Also, the fact that the coolant level is low is suspicious, although of course that could just be a coincidence.
To answer your question, the car has the GM-sourced G4 transmission. It has 96025458 written on the green tag on its side. After a lot of research, I went with Valvoline Max Life DEX/MERC ATF. On its bottle, it says it's recommend for use in transmissions that use GM Dexron II, III, and VI, and BMW LT71141, so it appeared to be acceptable stuff. Other people on the forum had used it as well. Hopefully this wasn't a mistake, but I'm skeptical of the "BMW magic special fluid" argument, especially when it's a GM-sourced transmission.