My Rice flatbottom .50 does the same thing. In my experience some days are worse than others, which I attribute to heat and humidity variations.
I wipe between shots. When I feel that "ring" starting to form, I simply run a wetter patch before the dry one. I used to use a damp patch, then dry, but have gone to a wet patch in the summer.
In my rifle the lube doesn't seem to make much difference. It still gets that ring of hard, dried crud after 4 or 5 shots. I am using Goex 2f.
If soaked, or wet patched, the ring comes right out.
When I clean at the range, I scrape the breechface first with the scraper. Sometimes nothing comes out, but it just takes a second. Then I'll plug the vent and pour plain water (or with a little Simple Green added) in the bore and let it sit a few minutes. I dump that out, run a few patches, and then flush it out again. Again, some days are better than others.
Best wishes and God Bless, Marc