What you said is what I ended up doing. The belt had already come off in the rather unconventional manner I mentioned earlier, and I needed to get it back on.
I did not notice much loosening of the tensioner pulley. Perhaps I did not turn the hollow tensioner enough. It did not move much at all, so if it is boken it is broken in the "tight" position rather thn the "loose," which I presume to be the preferable state.
When I reinstalled it I pulled the last loop on over the idler pulley above the alternator with just a bit of difficulty. Then I tightened the tensioner. The tensioner pulley went from somewhat moveable to not at all moveable.
The belt seems tight, by both feel and my ability to, once again, be able to turn the steering wheel lock to lock wiith just one finger while the car is idling, which indicates the belt is gripping the power steering pulley more solidly than it was before. I also heard that high-pitched groan/hiss that is normal on lock-to-lock turns.
My question now is whether the slippage was *more* the result of the loose belt, or the oily belt? There is some residual ATF fluid leaking from the pump, but not nearly as much as before since I replaced it with Valvoline with its special seal-swelling additives. I plan to drain it and use the Valvoline Synthetic PS fluid which I found, and which I understand is really good for seals.
All in all, it is clear now that my loose, slippery belt was responsible for 1) my battery not charging fully (belt not engaging alternator pulley) 2) overheating (belt not engaging water pump pulley) 3) "heavy" steering (belt not engaging PS pulley).
Hope the problem is solved for now..
2001 E430 4matic
Gone but not Forgotten:
1995 E320, 252,xxx miles, Black/Grey
1989 260E, 223,00 miles, Black/Black