The gaps just need to be below the copper. Realistically, anything that will get them there will work - toothpicks, small screwdriver, blunt scribe, etc. Cheap and/or old toothbrushes are handy for lots of small cleaning projects.
After you get the brush holder aligned, consider adding some reinforcement to keep it in place. Epoxy putty or auto-body filler will work; something that can be shaped without dripping off.
Roy