So, on the new barrel. Why not just buy a replacement 7.7x57 ... I can put you in touch with a fellow in ID who has maybe 150 barrels. He can match your arsenal so it should be minor fit up. Prolly $150, or less... He can supply bottom metal too
303Brit/311 bullets are not hard to come by and you reload
Or, if going new barrel, maybe something a bit heavier?
I actually have a 7.7 barrel, the one pictured is one i bought as replacement a while back.
Whats making me want to go with a new barrel is mostly that If im gonna pay for some one to fit a barrel it might as well be a contour i like better, and a different chambering. I also never really liked having more than one gun per cartridge, and my other 7.7 sporter fills that niche perfectly.
I actually have a few more options than i thought as to cartridges. I have the janky "06" length mag box which is ugly but works, itll take up to a 3.28 coal. I tried running 06 rounds thru the action with the bottom metal jist screwed in and they cycled fine. I can probably make a better version of the box that came with the gun, possibly get 3.3 coal.
The rounds im considering now are the .338-.358s, possibly a .35 whelen AI (mostly for the shaper shoulder to help with headspace). Only issue i see with the 35WAI is coal being longer.
Im open to ideas also.