HI CGB and others. Firstly thank you for the comprehensive explanations you have provided and it all makes sense to me.
In Europe the Jeppesen plates generally include a TCH ( threshold Crossing Height) based on the theoretical GP angle and the point the G/S impacts the runway. As the optimal TDZ is normally 300m from the threshold the 1:60 rule, for 3 degrees, puts the G/s 50 feet above the threshold. Consequently most 3 degree slopes, without any GA infringements quote a TCH between 45 and 55 feet.
As the aircraft descends along the G/S the crew make the decision as the BARALT approaches/reaches the DA minima. On the 3 degree path this theoretical point is 1200m approximately from the optimum TDZ point.
Therefore, unless the ground is significantly higher than the threshold, out to about 1km from the threshold, which would be highly irregular, the practice of setting a backstop DH 30 feet below the approach DH minima, works very well.
I have never operated in the US or much in very mountainous regions so this may not work everywhere. However, my natural sense of safety/justice would be seriously challenged if I thought at a theoretically correct DA (no flight path error) I was significantly lower to the surface than the procedures published DH.
In any event, getting lower than 170 feet from the surface IMC during the approach is probably close enough for me and I would really want to be going around at that point (accepting I will continue to descend below 170 feet momentarily in the go-around action). I may be a little naive in this respect but at a 500 fpm ROD I am a little less than 15 seconds from impacting the surface.
Interesting thread though that does challenge the concepts we all carry in our heads.