Minimum headspace on the Number 4 Rifle is .064", friend. The RIM has to go somewhere!
Max is.074"
I do not know of any "recommendation" for 6 (or any other number) thou between the brass and the boltface. The things were supposed to be as close to zero as could be made.
Part of the problem could be that very darned little commercial brass has a rim thickness of .063": the military standard which was supposed to be adhered to whenever possible.
You might measure the thickness of the rims on your "Remy" brass and see how close THEY are to spec.
You might also get yourself some DEFENCE INDUSTRIES brass from WW2. This is the stuff with just the date, letter Z and letters DI on the head. It is Boxer-primed, non-corrosive, non-mercuric and it is the best reloading brass ever made. It was also made in Canada. Dates run generally 1942 through 1945, although I am told that a bit of 1941 also was made. You run into it at gun shows; sometimes idiots throw it away at ranges. That's where I got my latest thousand. You might want to anneal it gently; it IS getting a bit long in the tooth.