@jpmcwjr. So, after removing dottle or ash, I run very hot tap water into the bowl and out the stem. Then a paper towel in the chamber, pipe cleaner for the stem, Q-tip for mortise.
So I took your suggestion to flush with hot tap water. I flushed the hell out of two pipes. Took the finish right off. LOL. Good thing I was planning on polishing it.
I prefer how my pipes taste after rinsing, so I'm in the rinse-club. Hot water will take beeswax right off, and carnuba after a couple of rinses. I just keep a jar of paste wax and re-wax them as needed.