Sure sounds like a transfer case issue. However, I am 99% sure that the later (LCI) models have a longer front driveshaft from the factory. Check the RealOEM part number and make sure they are different, which I suspect they are. I've got a 2002 E53 (Pre-LCI) and the last 7 of the VIN are: lh36976, which shows a driveshaft PN of 26207508629
If I'm wrong and you do have a shorter driveshaft I think you can find a used long one on ebay probably or a Pick and Pull. Also, many guys (myself included) swap in the Everbuilt longer t-case end splines, which you can get off of Amazon at
https://a.co/d/07VOS94. Not a difficult job and there is lots of info on it here. Happy to give you my two cents/experience if you want to go this route.
I was unable to find someone to balance mine after I had the splines welded in, but I detect no issues in my very un-scientific seat-of-the-pants vibration measuring system. The one driveshaft shop in town that would do it, theoretically, didn't have any way to secure the front diff side of the driveshaft to spin it. They wanted me to pull the yoke out of the diff, which seemed like way too much work.