Happy to chat it over, in Mitchell or otherwise. However, my concerns were:
a) By introducing the concept of Map Shift in your first posting, you were introducing a problem specific to FMS systems which does not have a parallel in GA GPS systems, and which does not have any bearing on the use of GPS in light aircraft for approach purposes. If the GPS is showing a RAIM warning, an Integrity warning, or is navigating in 2D mode only, then you don't use it for approaches.
Furthermore, you drew an unfavourable comparison between IFR approved GA GPS systems and airliner FMS equipment
Regarding light aircraft, if the GPS in a Boeing, or its map, can let you down, then do you really want to place all your faith in a couple of thousand pounds' worth of panel-mount kit?
FMS systems are approved for a whole range of operations that GA IFR GPS installations are not approved for... however GPS approaches is not one of those differences and the suggestion that a pilot should not place faith in an approved GPS installation on an approved GPS approach is misleading.
b) Your comments relating to GPS failure and the difficulties of executing an approach
'Leaving you part-way down an approach, with no accurate navigation information...
All the RAIM messages in the world won't help you find your way out of trouble, when you have no tracking aids available, nor the current ability to interpret them...
You fly the missed'... Tracking, just, what, to your next destination?
appeared to imply that this was in some way more difficult than executing a missed off (say) an NDB approach in the event of beacon failure and in the absence of any other aid. This is not the case. MAP is established by timing and ICAO approach design methodology assures the rest.
I hope this sets out the questions that I think arise out of your posting. FWIW, I think IO540 was nearer the mark than you give him credit for.
2D