You can get rails for anything that’s been mentioned. You’ll need a canted rail to get to 300 anyway.
I have 2 10/22’s right now that I would like to trade for Ruger Americans. I just prefer a bolt at this stage for everyone in the family who shoots.
I think the BXR and the 10/22 can do what you want, but it may take some work. I’ve had ejection/extraction issues with the 10/22’s. And I think they need a barrel to keep up. But, initial cost may be less and then you can build what you want. For close to the same money. Just my experience.
I have a friend who has the competition 10/22 and it hammers. With just about any ammo he tries. Have another friend who has a BXR and it can be very finicky with ammo. When it runs, it will keep up with anything. When it runs.
I know I sound bias, and I guess I am to some extent. The Ruger and CZ bolt actions have been good for me.