I have a 6mm Dasher with a 1-8 twisted Bartlien 5R in a Sendero #13 finished at 26.A un named powder will drive the 105g Berger hybrid at 3077fps.
A 6mm 105g Berger Hybrid at 3000+ is a wonderful thing.
This is on a fullon 1000 yard BR rifle.But its a total joy to shoot.
Thinking your fun gun in a 6BR with a 20 inch barrel will get to pretty close to 2800.We see straight up BRs on the line and they do pretty well.
To do what you want.
I'd think 6x47 Lapua.
A few more grains of powder and even the 20 incher should come alive...
Just excellent quality 6.5x47 brass....you cant get 6XC brass right now...

dave

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Only accurate rifles are interesting.