I read somewhere that you can soften water by boiling it, and decided to
do this as an experiment with my well water here in Crisfield, MD (about
1/2 mile from the Chesapeake Bay).

Before boiling, my water was 10 degrees (not ppm) general hardness, with
a pH of 7.8. After boiling for about 2 hours and cooling, it was 4.5
degrees general hardness and (this is the part that mystifies me) over
8.8 pH.

I don't have a test kit to measure carbonate hardness.

Any ideas what's going on here? If I add this water to my aquarium,
which is about 50/50 unboiled well water/distilled water with a net 5
degrees general hardness and pH pretty stable at about 7.8, is it going
to raise the pH of the aquarium by as much as I would intuitively think
it would?

As you saw there, it is backwards. boiling it drives off the disolved co2,
making it a little higher ph. when you put it into the tank, it will
re-absorb some co2 from fish etc. and balance out at what you have in your
tank now. All the boiling did was (far as good), kill and germs and
bacteria that may be in the well water. fwiw..