The 6mm Remington is based of the 7mm Mauser. The case is about 5 mm longer. IMHO You might have success with the shorter/ lighter bullets but the heavies will be seated long and need single loading. The 243 is a fine cartridge as is the 6mm Creedmoor.
The choice is yours to make, the Savage mags will go 2.940" +or-.
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