Ruger works fine and would be in the price range. Slightly janky and not super polished OEM but it’s modular. I’ve reached out to 1K with precision on a Ruger platform. I call this a entry level gun for long distance … that works. It’s a good platform to understand many of the ‘issues’ you’ll discover with precision.
Bergara has a model I think but it may be pushing the pricing. Weight is actually a good thing depending on your intent. If you’re going 6.5, the most popular application is long distance where you are mostly set-up and not moving around too much.
R700’s are sort of the benchmark but it’s entirely dependent on the smithing and component quality. I’d go R700 as a custom build once you’ve had a chance to get comfortable with long distance precision and some of the niggles that are personal preference. For instance, bore axis is going to be slightly elevated relative some of the other solutions. Are you able to overcome the muzzle rise to regain sight picture timely? Barrel swaps may get a bit more complicated, etc.