The BIG issue is the differing web diameters of the various brands: the original Remington virgin brass usually measures 0.463-.464" just above the extractor-groove (reamers usually cut .467-.467 chamber), while the LAPUA in my boxes runs 0.469 - .4695" (reamers usually cut .471-.473" diameter chamber). While the chamber and brass lengths can be an issue,
the relative diameters - throw in a sizing die - are the major concern. Determine which reamer(s) your smith has and obtain appropriate brass - bear in mind, anything close to the original Remington dimensions may prove difficult to find. FWIW, though, "too small", the Rem. 7BR brass does work well in a 'LAPUA' dimensioned chamber, the opposite, not so well.
Way back when, Remington expected us to make our 22/6BR brass from full-length .308 brass, which they sold it under the moniker, '.308UBR'. The UBR features small primer-pockets, & to accommodate forming, is annealed all the way down to where the BR shoulder would form - I still have a good stash and use for many wild-cats, and competition applications.

RG