I built a big sill for a bow window, using birch "roasted" by a local
mill to give it a dark brown tone similar to mahogany. Anyway, I
planed and sanded it to a finish that looked pretty darn good, and
applied a coating of linseed. The finish was gorgeous, but
unfortunately, a few thin spots of gal-oo that I hadn't detected
earlier showed through pretty bad.
A few days later, I sanded out the glue spots, and reapplied the BLO.

This is where it went South. The spots that had been sanded clean just
stayed matte, almost as if they just weren't taking the oil. I'm
wondering if the sanding process had some sort of sealing effect on
the wood, the oil/dust being ground right into the wood.

I could try and plane and sand it all, but I'm afraid I'll end up with
the same problem. I could also try to just flip it over and use the
other side, but I like this side better.

Any ideas on how I can save this?

Thanks