There is a discussion on Flyer Forums about GPS ILS. I understand you are unwilling to extend guidance below 500 feet but it raises the interesting question of how accurate/reliable GPS now is.
The impression you get is we are not allowed to use consumer GPSs for precision navigation because 1) there is no separate system that attempts to detect or warn of errors (like RAIM), and 2) there is no specific failure alerting system.
As regards 2), it is highly unlikely you would not notice something was wrong. As regards 1), maybe - for the UK - there is virtually no need for error detection because it is virtually impossible that there is a scenario that could impact so many different sources of data. Particularly any risk would be lower than eg VOR, NDB etc
You get the impression that typical consumer devices can now track twenty or more satellites from different constellations. This gives the possibility of a huge number of calculations. I am not very familiar with the types of error that effect GPS but you would imagine with a large of number of calculations, it would be trivial to filter out certain systematic errors (eg single faulty satellite). More than that, with so many calculations, you would think just taking an average would be entirely satisfactory.
So for a typical tablet, does SD simply get a single calculated position from the host device or does it have access to individual calculations, and if so does it do any processing to pick the best fix?