OK, then why have the requirements that prohibit GPS substitution when

picking an alternate for filing?

When you ask why, you are making the assumption that the FAA makes
rules for valid and comprehensible reasons. That's not an assumption
that is supported by the facts

Seriously, the logic, if you can call it that, is that GPS is an
unproven technology, and thus one should have a backup plan that does
not rely on it. The FAA would rather you rely on a 30-year-old ADF
receiver pointing at a WWII-era NDB transmitter.

Getting out of the alternate rathole, any thoughts about the general
rules of GPS substitution, specifically applying them to the questions

I had on the Minuteman approach?

The rules are clear enough - any approved GPS may be substituted for
DME or ADF on any approach except that you may not use a GPS to fly an
NDB approach unless it is an approach-certified GPS being used to fly a
published overlay. Now those are rules. Your question regards
procedures.

As a Part-91 operator, you can pretty much use whatever procedures make
sense to you - if it's not prohibited, it's allowed.

In your particular case, the DME is used in conjunction with the VOR to
identify the IAF/FAF (EGORE, 210 rad 20.0 DME MHT) and the MAP (210 rad
25.1 DME MHT). If you like, you can configure the GPS to point to the
MHT VOR and read distance just as you would off the DME. That would be
fine. Or you can configure it to point to EGORE, and call the MAP at
5.1 from there. That would be fine. Or you can configure it to point
to the MAP, and call 5.1 from that the IAF/FAF. That would be fine.
Or you could write yourself a flight plan that would take you to the
IAF and then the MAP, so you could get a readout of distance counting
down to the IAF/FAF, and then the MAP. That would be fine. And if
someone has already done that for you (in this case the manufacturer
who provided the software for approach monitoring) and you're
comfortable that he did the job properly, that's fine too. Use
whatever procedure works for you.

The question become more interesting when GPS is substituted for ADF,
especially when the NDB is the missed approach holding point. One
option (if available) is to use the missed approach sequencing provided
by the GPS for the approach monitoring function (some will even depict
the hold and tell you which entry to use) but anything you care to do,
up to and including setting up the display to read out the bearng and
distance to the NDB and flying the hold off the numbers is acceptable.

If you would tell us more about what kind of equipment you have in the
cockpit, we might be able to make more intelligent suggestions about
what procedures would be optimal.

Michael