IO540 (nice engine, btw)
That is a EGPWS that you are talking about, and they actually don't include the GPS, at least in the Honeywell set (I do some consulting for Freeflight Systems, who bought the aviation GPS licences from Trimble, and who Honeywell asked to program a basic unit as a cheap input for their EGPWS for any aircraft with no convenient position output available). They use whatever position information is available, FMS position being the most accurate which takes into account much more than GPS position.
We (Freeflight that is, not BCFT or Solent who I also work for!) can also sell you the radalt you prefer, although that has no forward prediction.
I see no need to complicate the cockpit by ever refering to GPS altitude. Keeping MSAs 1000 feet clear of terrain, 2000 in mountainous areas (due to venturi effect) is perfectly adequate to avoid terrain. Baralts have to be used for aircraft separation, and at the levels at which we have terrain in the UK are very accurate anyway (you pointed out youself that the high errors are at high altitudes). There is no need for GPS altitude in aviation. It is a lot less accurate than horizontal position.
M14P
GPS is not entirely reliable, and when it goes, it all goes! You can't change to a different system, except to go back to traditional radio navigation. Occasionally it even goes in such a way as you don't know for perhaps 2 minutes, which can be bad on approach. With an NDB, as long as you can hear the beeps it is working, crude as the system may be. In aviation known inaccuracy is much more acceptible than extreme accuracy with any question of reliability.
Reliability has nothing to do with measuring K2. That is all about accuracy, and if you leave a GPS there long enough it will give you an answer to the nearest millimetre or so (they are used by geophysicists to track plates).
The CAA is a bit over the top on its concerns about GPS, but the basic philospohy is right, and the US government and military are now moving toward that position. The FAA are in fact looking at combining GPS and Loran (yes, you read it right, Loran!) for a more reliable system.