A trick a guy showed me to remove the residue glue on headliner. Use a drill with wire brush disk on the end. Only took him 10 minutes and all glue residue gone.

 

That sounds good but the headliner is closed cell compressed foam, if you would break through the black coating, you would very quickly put a hole in it. I guess if it's a fine wire brush and with care it would work but after doing one myself, I'd be afraid to try it that way.