We’d already tried the mineral spirits and it didn’t spread but good to keep in mind!I would try hand planing with a sharp low-angle block plane instead of sanding. Sanding’s just going to make more dust.
As for mineral spirits, first try rubbing a piece of padauk scrap with a white cloth wet with mineral spirits. If any color comes off on the cloth mineral spirits might spread it to the birch.
Wow. Did not know that. History if full of things like this. Big fan of James Burke for his threads on history not based on the political/military timelines we had to memorize in school.Try white play doh. The stuff was invented to get soot off the wall, making it a toy was secondary. Or, try a lint brush that is the tape sticky kind that might work as well.