A friend has a 80" x 37" cherry table they let several candles burn
down on. It actually burnt out maybe an eight inch of wood. The top
is 1 1/4" thick, but I think sanding the damage out is probably
hopeless; presumably the wood will be discolored deep into it, and it
might be 3/8" to find clean wood. Turning the top over won't work
either, as the bottom surface is quite imperfect.
That leaves ripping the damaged 12" out, putting new boards in, and
sanding it down.
The problem is the joinery used. The top is all 2" wide boards that
have a sort of finger joint between them. It is flat for an eight of
an inch at the top and bottom, and then 4 pairs of fingers, each about
an eight of an inch. They are rounded, and project about an eighth of
an inch.

A few ideas come to mind...

1. If you have access to a wide belt sander, run the whole top through
the sander multiple times till you get down to good wood.

2. Rip the top into widths that will fit through a planer (12"
typically), plane down to good wood, then reglue the top together. Sand
and refinish.

3. If you do not have access to either of the above tools, you may be
able to build a "sled" of sorts to flatten the top with your router and a
straight bit. LOTS of passes back and forth, but it should work in
theory.

4. Flip the top over and try any of the above methods. Depending on
whether the top is worse than the bottom, this might be a good option.

5. 80" isn't that long. You should be able to cut out the damaged section
and replace it with a single board.

6. Assuming this section isn't on the edge of the top, the joinery won't
show anyway. Use scarf joints, or slots and splines to join boards
together. Then cut out and replace the damaged section.

7. Depending on the construction of the table, maybe you could just cut
out the damaged section and make the table smaller? For example, 80" x
35". It's unlikely anyone would notice a couple of inches difference.

8. Forget about repairing this top and just build a new one from scratch.

Anthony