You should be able to keep a Savage/Remage build under that $1,000 budget, but with pre-fit barrels running the .28 Nosler you may run into issues with chamber wall thickness limitations. The 7mm Rem Mag should be good to go either way though.
Feel free to give Mike Ross a call at (262)...
Unfortunately the smaller shank size of the Ruger Precision rifle precludes manufacturers from chambering in SAUM cartridges. If the chamber was cut to accommodate the cartridge, there would be insufficient chamber wall thickness to accommodate the pressures encountered with that load.