Oops. I'm not cleaning it with mineral spirits. I'm using denatured alcohol.

Yup, sounds like shellac.

Which is a terrible finish for wood subject to wet/moist conditions.

If you want to finish without changing the color, use a water based varnish.

If adding an amber tint is desirable, use an oil based varnish.

Not necessary to strip off the shellac. Varnish binds to shellac very well. Once you get the dirt and gunk removed with the DA, it's ready. Varnish is the way to go. General finishes makes an excellent water based varnish. For traditional oil based varnish, try Waterlox.

Get some nice China bristle brushes for the job. If you use the waterlox, soak the brushes promptly in turpentine to get them clean. Use a wire brush to get the paint brush bristles clean and straight. Good paint brushes should last for many years if cleaned properly.

Thanks guys. Whatever it is, it's coming off entirely with the alcohol. This stuff is incredibly dirty!

"Once you get the dirt and gunk removed with the DA, it's ready."

If you are using denatured alcohol on shellac you are removing the finish.

Pint thinner is the 'go to' cleaner for finishes since it dos not damage them unless you leave a lot on for a long time (it usually evaporates unless it is covered with something).

Thick shellac finishes can provide adhesion problems for varnish.
Thin shellac finishes are rarely a problem if they are clean