When my former ’91 300TE 4-matic needed parts, on a few occasions they sometimes took a couple of months to show. Especially parts for the 4-matic system. The transfer case, in particular took about 3 months to show up. I can’t speak for Barrier but my experience with the guys in Seattle is that if they said they’d do something they’d do it. BTW Mercedes picks up the tab for the rental; not the dealer, so I’m all but positive you’re okay.
Any chance you have my former 'TE? Does yours have a Sony CD system rather than the Becker?