Got to the bottom of this with my dealer.
So BMW has issued a service bulletin for the doors as gpitts mentioned. SIB 51-16-14. For this bulletin they replace the bowden cables (these are the cables used to close the doors and tailgate according to my service advisor) and clips.
The bulletin doesn't fix the problem however.
So my dealer had to open a PUMA case direct with BMW. BMW engineering took ~2 days to respond once the case was opened, and overnighted the parts to my dealer. In case anyone else on these forums runs into this issue, the PUMA case number is
60320058. They replace all 4 door actuators with the newer model.
Thanks to these forums, I clued my service advisor on to the actuators when I dropped the vehicle off, but they were obligated to try the SIB first. I actually got pretty good at repro'ing the issue so they were able to do the same to verify that the SIB fix didn't work.
In case anyone else runs into this, just reference the PUMA number above when speaking with your service advisor. Hopefully BMW will just issue a new service bulletin for this issue, as SIB 51-16-14 doesn't fix the problem.
While my X5 was in the shop, I also had the HUD fixed (SIB 62-03-14), the drive assembly for the bolsters in the driver's seat replaced (the bolster would buzz every time you used it), and the drive unit for the power tailgate replaced (it would also buzz in use). I was going to wait for the first service to get these items fixed as they're all pretty minor, but figured I'd get them addressed while it was in the shop. Our X5 is back home and running good again!
