I fly RNP approaches in a single engine GA aircraft.
In most cases, the airport still has at least one conventional approach for the targeted runway and the RNP and conventional missed approaches are very similar if not identical (differing only on the DA altitude).
And in most cases again, there is no obstacle clearance issue on the missed approach path.
Thus, I always also prepare the conventional missed approach as a backup and, if RNP capability is lost, it's mostly a non-event with a message to the controller stating that RNP capability has been lost and that we revert to the conventional missed approach unless they prefer to give us vectors.
As a counterexample, I fly to Colmar Houssen LFGA which has high ground in the westerly direction.
The airport has kept NDB approaches for runway 19 but only has a RNP approach for runway 01.
For Colmar and specially in IMC, I always write down the safe QDR limit to STR VOR (Strasbourg).
From memory, I think that it's R196.
If I were to loose RNP capability on a RNP 01 approach, I would fly the start of the RNP missed approach using heading, warn the control, and then join the HO hold (NDB) while climbing and while keeping an eye on the QDR to STR.
I don't have the special authorisation for Innsbruck LOWI and I don't know what should be planned for a GPS outage as the LOC R RWY26 approach has a missed approach that uses RNAV with RNP0.3 .
I guess that Innsbruck is only accessible to aircrafts that can fly with an inertial system that is independent of GPS signals.