When I returned to the scope after concluding that the mirrors
were perhaps shifting and losing collimation, I expected to find
them still badly out of line. I was surprised, then, to find that
the first test image showed good stars in all corners (thus indicating
that I am very close to proper collimation of the scope).
I took another image to confirm, and the stars were very elongated.
How could this be?

I checked the focus, and it was clearly off, whereas it had been in
perfect focus just minutes earlier. So, I refocused, and the next
image showed good stars again.

I watched the focus carefully for the rest of the night, and it seems
that there is a frequent (though inconsistent) slipping of something in
the focuser mechanism. The focus always had to be adjusted "in". Since
this problem can arise from one frame to the next, this may account for a
good deal of my difficulty in collimating this scope (since the focus,
and thus the star shapes, may change between when I focus the scope and
when I take the first image to check collimation).

With direction from Starizona, adjustments were made to several bolts
that affect the stability of the focuser, and I believe that this problem
has now been solved.