Yep it'll do the job, both rifle and cartridge, depending on what you mean by stretch.
I'm thinking that possibly wind may be more of a factor than distance. Thus heavy for caliber bullets would be appropriate. Factory twist may be a limiting condition here.
What about a 243 in the same model. That would help some with possibly more barrel life. If I recall correctly my huntin' buddy's REM 22.250 loaded quite warm, went belly up at 1500 rounds.
Even better would be the 243 Ackley Improved. There's a fella down the road from you that does a heck of a job on the AI cartridge. This is kind of dreamin' though.