First off, you are choosing the wrong brass. Compare a 300 Win Mag & a 308 Norma Mag case side by side. See the difference?
Now compare a 7mm Remington Mag. case & a 308 Norma Mag case side by side. Can you tell the difference? I thought not.
If you cannot find some 308 Norma Mag. brass, grab some new 7mm Rem. Mag. brass, expand the case necks & you're good to go. No using too long brass which must be re-formed & trimmed and will result in the case neck being formed from the thicker brass from the shoulder / body. I've been doing this for over 40 years. If you can't find 7mm Rem. Mag. brass, look for some 338 Win. Mag. brass.
After Winchester brought out the .458 Win. Mag. in '56, the .338 Win. Mag. in '58, then the .264 Win. Mag. in '59, the next logical step was a short .30 calibre magnum cartridge. BUT, Norma introduced the .308 Norma Magnum in '59 along with its bigger brother the .358 Norma Magnum in '60, both of which were designed by their Chief Ballistician Nils Kvale [whose first short Magnum Belted cartridge was the 8x61 Kvale Magnum in '49], screwing up Winchester's plans to legitimize the older .30-338 Magnum wildcat. They had to go back to the drawing board, coming up with the .300 Winchester Magnum in '63. In the interim, Remington came up with the 7mm Remington Magnum in '62, thereby filling up the mid-calibre short magnum cartridges.