Perhaps we are talking about different conditions when we refer to the
GFCI tripping. Here is my understanding; if I am mistaken, please let
me know where.

Receptacle ground wired to LINE neutral: Normal downstream
Neutral-Ground detection will still work; the GFCI will not trip on
power up unless there is in fact a Neutral-Ground interconnection
downstream of it. In the event of a device fault between the Hot and
the EGC, the GFCI will trip, as the return current bypasses the GFCI.
In the event of a fault between the Hot and some external ground, the
GFCI will likewise trip.

OK. Don't see any problem with your analysis so far.


Receptacle ground wired to LOAD neutral: This obvious downstream
Neutral-Ground connection will not be detected and the GFCI will not
trip on power up, because there is no upstream Ground to complete a
circuit.

OK.

In the event of a device fault between the Hot and the EGC,
the GFCI will not trip, as the return current still does go through
the GFCI. In the event of a fault between Hot and an external ground,
the GFCI will still trip.

Yep!


So if an appliance has a Hot to grounded chassis fault, then the GFCI
will trip in the first case and not trip in the second case.

Yep!

Of
course, the circuit breaker may trip in the second case; if not, then
the GFCI should trip when a person touches the chassis and provides an
alternate path to ground.

Yep, again.

Note that I'm not a proponent of either of these wiring schemes, I
just want to be sure I understand what would happen.

Good.

The truth shall set you free.