I use
a 410 or 28g mop and usually put a large 2.5"-3" square patch over it then insert it into the chamber and turn.
The mops last that much longer and every time you stick it in with a clean patch on it you are not introducing foreign matter into the chamber area.
I just use lighter or Naptha on the patch. Evaporates without needing to be dried out.
For the lug area and raceway I have a tool made to take Dental rolls. Put one on, slide it down the raceway, spin in the lug area and remove. Repeat if necessary.