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The colors seem to have come out of alignment on my tv. For example, if
I have closed-captioning running, I can see a "ghose" of red above and
blue below that white lettering.

The term for this is convergence. Or in your case, misconvergence.

Possibly related, for a few weeks before the the "focus" went away, the
tv was "humming" (sounded like 60HZ noise to me).

This may have been the yoke rattling at the vertical scan rate.
The yoke is a molded and glued mess of ferrite, sheet metal, and
plastic wound with specially shaped coils of wire that fits over
the neck of the CRT, and has the job of deflecting the electron
beams to generate the sweep (raster).

Part of the factory convergence procedure involves warping the
yoke to move the center of its magnetic fields into the best
position for the colors to line up. They jam rubber wedges
or strips of cardboard under it to hold its shape. With age,
the plastic can sag or crack, glue gets brittle, and sometimes
things get loose internally.

There is a good chance you would have to replace the yoke to
get it right, and they are pricey. The alignment procedure is
best done with a pattern generator, and can be tricky.

I'd just as soon try to fix this myself if someone can give me some
pointers. I'm handy with digital stuff, but haven't done any TV repair
before.

If you are lucky, one of the rubber wedges may have fallen out
from dried-up glue, and you can jam it back in place and improve
convergence. The fates are not usually so kind. You can also
fiddle with the rings on the CRT neck, and maybe improve it a
bit. Make note of their original position so you can start over
if you make things worse. This is about all the average do-it-
yourselfer can do.