Gouge. Sanding clogs, and, if you press, liquefies it to flow in further. Imagine the difficulty will come in mounting the piece for the job. I'm sort of lucky, because I use mortises on the bottom of mine, and if it doesn't sell with the finish/thickness it has, I re-turn it.
Either that, or a lot of agony with solvent soaks and rinses prior to your next sanding.