you've destroyed the glaze - whatever you patched it with would look horrible.
...
Anything that you use to build up the bottom of the bowl will also have
to be coated and will look horrible.

Why is that? Is the commercial tub-and-tile epoxy paint really that
bad? I've never tried it, but have a new, unopened "tough as tile"
brand batch left from the previous owner. Would this not work to
reglazing any exposed area that was deglazed, and/or for building up
the bottom?

It's the type of project where you could easily spend many hours or
days making the thing look even half way decent.

Yup. But I think of it as a kind of hobby, or challenge. People spend
many hours and days doing lots of things. Besides, I'm cheap, don't
have terribly much money, don't like to spend money on things that I
can do without (i.e., I can live with the existing sink rather than pay
$100 or more), don't like to throw things out, and so on. I'm not
unrealistic, though: if it ain't worth it, I won't do it.

I can get a custom made bowl for around $100 or so. But the
tub-and-tile paint is free, and the existing sink is already there (and
the hole in the counter was custom fit just for this bowl too!).

Thanks for the comments, though!
-Kevin

It would be better to
have a garage sale or sell stuff on eBay to raise money for a sink that
is meant to be a sink. Call around to a local college or ceramic arts
store. You might find someone willing to make you a simple bowl with a
hole for fifty or a hundred bucks.