Bat, Borden, Kelbly, and Pierce would be my suggestions for a smooth custom action.

I'm a huge 6br fan. My Nesika J 6ppc wasn't getting used much so I had a 8 twist 6br barrel spun up and found 50 lapua brass with the rims cut down to fit the ppc boltface. 105 moly Bergers for LR range practice.
Used short range benchrest guns are always veeerrryyy smooth and are often cheap compared to building your own new rifle.

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This is my latest 6br. I had an extra 700 SA and bought a used 6br barrel. I call it my 6BR 700 Parts Gun. It shoots. 66gr Woodwards.
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If you need brass, champions choice has lapua in stock for a good price. Good luck.