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.

Getting an exact match is too much to ask for, but I can't find anything
even close. Any suggestions, either on the cutter or alternate methods? I
will take a router bit, a shaper cutter, or maybe even a molding head for my
table saw.