Use the steel wool as backer for caulk. Fill hole with caulk in two or three built up layers, let each set a while B4 next, a big one shot blob may fall out. Any good quality paintable caulk that will adhere to stone and wood will do.
"steel wool, leaves a bad taste in" my mouth too. I find that if i drench it in jalapenos and cheeze whiz it is a bit more palatable.