Ok. Got it figured out. Turns out, in all the permutations of mix and matching old vs. new parts, I got the motors mixed up, and I was using the new motor with all the other old parts. The way I discovered it was analyzing the length of the motor assemblies and it so happens that the new motor's shaft is ever so slightly longer, causing the bind. I didn't look into it before now since I thought I was already using the old motor which worked before, and it should have been right. Doh!

Anyway, thanks for your help, and for those doing this repair in the future: be advised that these repair kits may not match the OEM quality very well. I just tried it because it was $40 rather than $160 for a used OEM part that may have the same issues mine did. I could definitely grind down the tip of the motor a bit to make this work, but I'm just gonna keep the original parts and move on with my life.

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2006 X5 4.8is