I'm not entirely convinced that the use of either radio altimeter or GPS altitude is going to be the total answer to the problem.
If we are talking about an RNP LNAV approach and decide to publish a radio altimeter height to be expected at the FAF then we would have to be confident that the terrain variation within a rectangle 0.6 NM wide and 0.48NM along track wouldn't change that value by a significant amount.
With reference to using GPS elevation, the FMS system that I am most used to (Garmin 750) calculates Geometric Height as an approximation to mean sea level. The Geometric Height is based on the WGS84 geoid EGM96 which is a global geoid model giving a 'best fit' for the whole globe rather than a more accurate 'local geoid' model. As an example my old hunting ground of Gloucestershire Airport publish a 'geoid undulation' (variation from EGM96) of 161ft in the AIP. Would that difference in your GPS elevation be enough to give you confidence in the barometric altitude indication?
Cheers
TeeS