For reassembly, most of the steps above can just be followed in reverse. Just a few points...
The center gear needs to be installed with the main shaft gear at the same time, there's not enough room to install them separately. Here you can see I installed the main shaft and had to pull it back out.
Also, Don't forget to install the plastic oil sump pictured here, I had it almost completely reassembled when I saw that piece on the table and had to pull everything back out to put that in. Notice it's missing above lol
Make sure the snap ring for the main shaft is seated all the way around and squeeze it together to confirm
When reassembling the clutch assembly, a couple of clamps is necessary to squeeze everything tight enough to reinstall the snap ring.
I used RTV Black for sealing the two case halves back together. I'm sure the German spec calls for something else. 12-24 hours drying time is probably a good idea
Once sealed, the halves can be aligned and tapped together with a rubber mallet.
There are two different lengths of torx head screws used to seal the unit. My crude drawing specifies what goes where. I think I torqued to about 15 lb-ft in a star'ish pattern, though I didn't find an official torque spec anywhere.
Almost done, onto the fun part, reassembling the output flange. Here you can see my old beat up flange next to my new one
When you order a flange, you get a bunch of shims, each one is 0.1mm thicker than the last...
So I figured, just measure the old shim to start with right?
Turns out, the old shim size was way too thick to get the snap ring back on for me. Here's where the fun starts. You have to start with a shim that is too thick, and then work your way down one by one until you find the thickest one that can be snapped in. (Keep in mind these don't just slide on easily, and the output flange has to be pried back off each time to remove them. Probably not the worst time to open another adult beverage
This took me about 5 tries and about 45 minutes)
And that's pretty much it. The case held a maybe 600mL of fluid. I filled it under the car, but you could probably do it on the bench and just check it once installed. BMW instructions say to drive 600 ft and then recheck the level again. I did this, but the level didn't change. YMMV
When reinstalling the transfer case, Weicon Metal-Free High Temp Anti-Seize is called for on the transmission output shaft. I ordered a bottle (which arrived 3 weeks later, difficult to find in the US), but luckily the output flange comes with a small tube of the stuff which was enough for this job.
You should reset the transfer case adaptations using the ISTA+ software when this repair is complete. Not sure what would happen if you left this step out, but it makes sense that it may need to relearn some things.