Go to www.savageshooters.com
and a guy named "PAHog" has a custom rifle
6mmbr just like you want in 10 twist. Look in the classifieds and under "savage rifles and parts"
However, if you are shooting Fclass, you must only be shooting out to 600. The Fclass guns in 6mmbr are all 1-8 twists.
In a 1-10 you might get the berger/sierra 95 grain bullets to reach a 1000 and be stable but questionable
Northlander on the same site, sells the savage fclass guns in 6mmbr for around $950 new.
Now if you want a 308, then again the savage 308 fclass guns are 1-10 and shoot very well for the same $950.