I think you are on the correct thought path.
When the first shot and paper ctg., shoot into the same group, it's about perfect.
I found with my .69, that the first shot loaded with cloth patch with the hunting load and lube, goes into the
same group as the rest, whether they are patched in cloth or "dry" paper.
As well, I should add, with the snug paper ctgs. I used, they never smoldered or caught fire.