I dont have a BLR, but, I do have a Savage 99 in .308
I use standard (Hornady) dies in a single stage press(RCBS).
As long as I make sure the dies are set correctly and I am careful to run the cases ALL the way up, I get along just fine.
However, if I were to go to a progressive, ( A Dillon 550, is calling its sweet siren song to me) I think I would go with the small base dies as I recall reading somewhere that progressives don't re-size as fully as single-stages do.