Sierra, Hornady, Nosler, Speer, Barnes, Lapua, Lehigh, Remington, and Winchester all offer quality .310/.311 bullets. So that won't be a problem.
However, building a .308, 1:16" barrel with the Lapua chamber would also prove very accurate. There are a number of .30 cal. benchrest cartridges that are shot with 120gr to 125gr .308 match bullets and they all use rifling twist from 1:15" to 1:18" with excellent results.
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