If I am remembering this right (which its a distinct possibility that I am not), Scotch Tape is about .002" thick. the 308 GO/NO-GO are .004"-ish in difference. Try two pcs of tape, and then 3 pcs.
I always set my headspace up as you have with your model 12 with just one pc of tape. Little more snug fit and little less room for stretch.
If you are reloading I would definitely keep the brass separate for each rifle.
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