Robert, re GPS geometric altitude errors you should contact Don Bateman.
We probably met during the reporting phase of the ECIII program – to CAA and Gov. The final ECIII report provides examples of risk boundaries re ground contact during go around, but only from 50ft.
At that time (1979) and subsequently, the UK CAA used a fog model which I believe supplemented ECAC doc 17 to approve operating minima dependant on aircraft type. Although complex, the model appeared to provide a very realistic first point of contact and good visual segment information. Again I believe that the model may have had a height loss component; or perhaps it only modelled the basic equation similar to the one which you have.
For a cross section of incidents that might have involved altimetry – failure to set QNH; see
Celebrating TAWS ‘Saves’: But lessons still to be learnt. My continuing investigation into these types of incidents suggests that QNH error, or failure to reset the altimeter, is still a very common error. Although not directly relevant to your question, the problem is related to modern aircraft systems particularly where QNH is used as the datum for VNAV approach waypoints (the majority of cases). Thus, just one small crew setting-error (or failure to cross check), it can affect both main altimeters and the NPA vertical navigation, which may have a visually powerful visual display providing the crew with even greater false confidence in their geometric position. Geometric altitude would provide a useful alerting system for such errors, even if it may not be sufficiently robust for primary use.