I put a patch in a cleaning loop, soak it in shellac, run it down the bores, then wipe the breech and muzzles. Let it dry, and repeat, twice.
It does seem to change with the heat of boiling, but doesn't come off or appear to break down. In fact, it seems to get very tough. I remove it by running a patch soaked with denatured alcohol down the bores. After it sits for a bit, I run a brush wrapped in steel wool, powered by a drill motor, through. I've made a rod that takes standard American brushes, with a guide that fits in the chamber, for this type of stuff.
Steven Dodd Hughes mentions some type of paint for this purpose when fume rusting. I'm thinking of trying that, as it may be easier to remove.
As far as getting any on the outside. If I had any doubts, a rag with a little acetone on it solves the problem.
Interesting that you plug the bores, but need to lap a bit when finished. I wondered how one could always be certain of a water tight fit, so decided on coating.
I don't think the plugs would be required for using logwood either. I'm not aware of anyone who plugs to hot tank single barrelled guns. You just wind up with a blued bore, which disappears quickly after a little shooting and cleaning. I would think the same true of logwood. I've only used it in the context of scalding browned barrels, and hadn't noticed the bores picking up much, if any, color from that process.