Even if you hadn’t missed the service the parts aren’t available, the same will be true for the MK 10 at some point, if you need a piston that will be that.Mk 10--also 30 years old and that got serviced just fine. Missed service was in 2014 when my mom was very ill so I had other things on my mind. It has been serviced annually since.
These can be kept in service but not by an “authorized” shop, your LDS is just following the rules that the “factory” has placed them under to keep that authorization.