Any tricks for getting the stud back into the wheel carrier? I'm pretty sure that it shouldn't be this difficult. Everything this is aligned, but it just won't get past the lip. I'll try to post pics.

__________________
1995 E420 152k
1991 300D 2.5 348116 daily driver
1992 300E 2.6 196k-work in progress(head gasket)
2002 BMW 745Li 93k

It is a very tight fit; I assume you did not completely disconnect the wheel carrier from the shock and steering? Now it's sort of hanging above the ball joint and its stud?

As has been mentioned the receptacle in the wheel carrier needs to be perfectly clean, a wire brush in a drill is a good start, but that will only get the surface rust. If you have a dremel or other die grinder with a stone that can reach up inside there you can use that or you need a small file or something similarly hard to scrape any rust too thick to wire brush away. Make sure that the compound the factory installs into the slot which hardens over time, is fully removed and not protruding into the receptacle

The FSM recommends against it but I haven't found any other way but to place a cold chisel into the slot and hammer it to spread the receptacle enough to allow the stud to slide into place. I try not to go crazy but it usually takes at least 4 or 5 - 3 lb hammer blows to wedge the chisel and on occasion I've had to repeat that. I'm in New England so my strategy is to completely remove the wheel carrier to facilitate this pre-assembly prep work easier, down south or out west maybe one can drop the LCA down and get things back together but not around here!

You need the receptacle cleaned and opened because if you try to use excessive force to put it together you can damage the ball joints cup by putting to much downward force on it as you try to force the stud into position. Good Luck!