First, the armrest on my car (1992 300E) slides over a couple of threaded rods sticking out from the side of the seat, onto which a couple of sorta-locking nuts are attached (difficult to turn even when not tightened). You get to the nuts by removing the little plastic cover where the armrest shaft attaches to the seat. Easy job once you figure that out. Luckily I gave up on removing the seatback before I destroyed it.
So I detached my armrest and sent the whole thing back to GAHH with a recap of my concerns.
I got it back today with the cover installed. They reused the same cover I sent back to them, but sewed it on permanently on the sides.
This resulted in a much better fit along the reverse seam, and hides the interior foam where it was visible before.
Still can see some raw leather edges unlike the factory version, but much better than before: