My first .340 was right at 8.25 with Conetrols and a 3-10 Leo. I had a 4.5 weight Schneider on it cut to 23" and I used for a lot of chucks and pds and yotes. Spose with a sling and rounds it was close to 8.5 lbs.
As a hunt rig I'd not want it anymore than 9 lbs at most all up (scope, sling, rounds). I'd want a stock that was in the 27-30 oz range at most and the mzl dia somewhere between .65" and .7" at the most.
No way no how would I do a break on it but I would go for magnaporting on it.
Personally I'd do a RUM or a .340 b4 I did the Lapua but that's just me.
Best of luck to ya
Dober