Welcome
I think your thoughts are pointed to a good way...

I agree that the problem must be either the DVD itself is bad, or the DVD transport/reader is bad (MK4 mechanism)

Have you tried a cleaning CD/DVD?
If your MK4 system manages the v31 CD upgrade well, you'll solve half the potential problem
After that, make a copy of the NAV map DVD, in order to be sure that is is re-written and possible defects have been corrected...

If everything fails, a new MK4 unit could be your next buy...!!!