Marlow,
That's a fine little rifle you have there. I recently got a 110FP in .223 that doesn't appear to be have been shot very much. 4th and 5th groups @ 100yds measured in the low .3's. Not really benchrest material, but pretty good right after having neck fusion surgery.
The .300WSM is very capable of going the distance your asking. Some of these guys are shooting it to 1K now. With a little practice you should be all up in there.
Does yours have the "Tupperware" stock on it? Mine does and I'm waiting for my bedding material to come in so I can spruce it up. Good luck. Johnny K.