Hey J, well you seem to get me today....
If the boards behind the new upholstery were replaced, the panels usually have small cut-outs where the screws will come though. And you are correct, that MB does things right, and that the pulls are bolted into the door itself. There are four holes on the door frame (2 up 2 down). You should be able to see them (both the holes in the door and the cut-outs on back of panel)...with the door card off. If it's already on the door securely (ie the other chrome what-nots are in place), you have two options:
1. remove everything, thus allowing you to lift the door panel off, see the holes, and perhaps do some measuring to get close to lining up the handle screws. You can poke a very small hole through the uphol. to get lined up for the final screwing. Its a little nerve wracking but once one is in place the others line up.
Option 2 is to do it all with the panel in place. You would need to carefully measure and push and prod a bit until you find the holes. If you had some general measurements from others it might help. Either way, you have to have the four screws, and small washers. In my case the hole sizes have changed over the years -- so my screws are a bit hodge-podgey. Yours are probably correct. I can get the part numbers if you need them.
The chrome caps on the door pull cover quite a bit and so you have a little room for poking to get the screws lined up. Good luck! and look at the bright side -- early cars like mine had pulls on both sides!! Twice as much fun...