I recently used a Savage 11VT .223 to compete at 600yd. The Savage factory 24" barrel has a 1:9" twist, so I was limited to a handload employing the Hornady 75gr HPBT Match bullet. It performed quite well at the distance, and would probably have worked well enough out as much as 100-200yd beyond that. Since can't shoot that far locally, I can't develop reliable handload performance data at the extended distances.
My Granddaughter shot the same competition alongside me using the same handload in a Stag Model 6 Super Varminter, witch employs a 24" 1:8" barrel. I was unable t complete my matches for health reasons, but she finished up with 3-20rd heats through the day, and had no issues. I believe I could have substituted the Hornady 75gr ELD-Match bullet, used it in the Stag, and probably had a combination that competes successfully against the 77gr bullet, possibly for as far as 1000yd, maybe not.
All these conjectures are missing one key point. The .223 is highly constrained when operating at that distance. Any healthy 6.5mm system is going to eat its lunch out there. But if I was going to do it, the Stag and the ELD-Match would be my candidate.
I could also spin on a L-W Savage Varmint drop in barrel with a 24" barrel utilizing either an 8" or 9" twist on the Savage 11VT, and still come up with an implement costing around $1K without the optics. A Mueller 8-32x44, Vortex Rings, and a Weaver 20MOA steel base would probably come in under $400 atop that. For the Stag, I'd skip the base and mount the scope right to the rail with Burris extra tall 30mm Signature 'Zee' Rings and 20MOA worth of offset bushings.
Hornady also sells an 80gr ELD-Match bullet, G1 BC .451, and G7 BC .221, pretty fine stuff. 24.4 gr of Varget is Hornady listed at 2750 fps in a 5.56 chambered 20". I'm going to give a SWAGestimate of the 24' barrel getting nearly 100fps more velocity. Using the Hornady 4DoF calc, I get a 1000yd velocity of 1226fps at 80 degrees and Phoenix's 1200ft altitude, using 30-31MOA over a 200yd zero. My local altitude is 4800fps.
As for $2K and $3K options, I won't spend that kind of money on a rifle when the Savage 11VT and Stag Model 6 perform as well as they do for me.
My L-W 28" 1:8" Savage Varmint 260 Drop-in was my goto F Open 1000yd competitive barrel for several years back in the early-mid 2000's, and has convinced me that for the Savage, their barrels are the way to go.
Greg