To answer your question directly, the 7mm family is an excellent cal for LR hunting INSIDE 1000yds. I would look at loading H4831SC or H1000 under a 162gr SST or Amax lit by a Fed 215m primer (expect 2900 to 3000fps). Cases sized with a Lee collet neck die. Seat bullets as close to the lands as you can and still feed from the mag, if desired.
Odds are you will be able to get this rifle shooting 1/2" or less at 100yds. It would also stay inside MOA at 500yds.
To determine how far you can use this for LR hunting, determine how far you can hit a milk jug 100%. This is the size of the kill zone on the average deer. Larger animal, larger kill zone.
My guess is that from a solid rest and ideal conditions 700yds should be possible. That may be much further then you should hunt, at least for now. Get a Leica rangefinder and a scope with consistent turrents. Make a drop table.
Practise ranging, dialing up, and hitting your target (milk jug). When you are so comfortable with doing this, practise when the weather gets windy or lousy. A real eye opener about distance and accuracy under field conditions. Don't be surprised if you max range drops by half or more.
Be honest with yourself and your skills. They will most certainly improve with time and practise.
I would not hesitate to use this combo on deer to 800yds. Under hunting conditions, that is a mighty long ways.
Jerry