66, I agree that break action rifles & rimmed cases belong together. The 307/308 setup is a real sweet deal. I am one who believes that no case shows it's full potential until it is fireformed to the chamber. I have had FTF's with my 358 Win. in a bolt rifle until the cases are fireformed, but after that, no problems. You probably know that using one of the fireforming methods can solve your FTF problems. Probably the most effective method is using a starting load with the bullet touching the lands. But I have had good results flairing the neck of my 358 Win. case necks with a LEE Neck Flairing Die, a load of Universal powder, topped with a Toilet Paper wad, & this saves a bullet. Once I have fireformed a case with this method I have not experienced a FTF. I flair the neck to the outside dimension of a fired case & this provides enough resistance to hold the case back.
But your rim idea has great merit & I'm sure there are many out here with me waiting to see your results. Good Luck ! :