Boy, that's a tough one.

I think I'd be tempted to try this:

Soak with an enzyme cleaner and let dry. I know it just makes the stain worse, but you don't want to encourage the odor to stick around.

Sand black spots until varnish is gone.

Try a wood bleach on the stains. This is NOT regular bleach.

A little more hand sanding and several coats of varnish might do the trick. Otherwise, I'm afraid replacement is the only option.

If you try it, please let us know how it works for you. I opted for laminate to avoid a lot of black boards.