Phil, they actually do make tools that will clean threads that aren't a tap or die. This way you don't cut material away, just clean what is there. Pictured is the low budget versions.
As a career machinist I use taps. Lots of them. Starter, Plug and Bottoming. To get them started in the thread so you don’t cross thread them, I try to clean out the first thread with a pick. I’ve had pretty good success doing it this way.
I have made cleaning taps by cutting a slot on both sides, in line with the length of the bolt to allow the crud someplace to go.
