I think the best solution for removing grease from wood will probably
be a weak lye solution, not so strong that it attacks the wood, of
course.  Lye will saponify the grease and oil quickly -- keep it
scrubbed up and refreshed, and then neutralize it with white vinegar.

Solvents just trap a portion of it at a time but don't make it go
anywhere.

Craig Brougher