Sounds like the scratches are pretty deep. I wouldn't want to take off that
much of the table surface. If you don't mind seeing where it has been
repaired (if you live in snow country anyway) find a shop that tunes
downhill or xcountry skis. Theses guys use a compound to repair ski surfaces
called P-Tex that has different colors including clear that can be melted
into the scratches that will level them up and stand up to minor scraping
and sanding then just refinish the entire tabletop. Homer Formby used to do
the same thing by melting a similar color crayon into the scratches but that
is only cosmetic, P-Tex will take some abuse.
OR
Find a woodworker in the neighborhood and see f you can get him to do a
dutchman repair where there is a section of wood removed and a new matching
piece of wood glued back into place. If done properly a dutchman adds
character to the piece.

Knothead