Like you I have shot a good many deer with 270 win farthest deer I've shot was with a 270 at 300 yards but I do not own one any more (had to sell because of surprise bills) also the one I had I lost 3 deer but later after alot of research i found out it was due to old bad ammo and being not more than 15 years old but I still have alittle bad taste in my mouth from that and I would go back to a 270 win or even a 270 wsm if I got some real good facts on what bullet/ammo to use.i would like to go up to a magnum caliber but ammo in my area is pricey but 1 or 2 boxs of ammo a year wouldn't be that bad
I'm going to go out on a limb ans say "Don't buy a new rifle". Not right now. Magnums are more expensive to shoot, have more recoil and much shorter barrel life. This is what I would do if I knew then what I know now...
First, join a gun club with long range steel targets.
Try it for a little while with your .308 set up the way it is now.
Learn about dialing, and buy a scope you can reliably dial for your .308. Doesn't have to cost an arm and a leg either.
Buy a Kestrel and a LRF. Learn to use them.
Practice as much as you can on those steel targets. Save all your brass.
By now, factory loads costs just too much and just aren't as accurate as loads taylored to your rifle, so it is time to learn to load.
Practice the whole system as much as you can.
Now. Buy the long range rifle of your dreams. You will know exactly what you want, and be deadly with it.
Rebarrel your now worn out .308. Keep it .308 or .260 or 7-08. Use it for your practice rifle and keep shooting it. Shoot the big gun just enough to learn it, and stay used to it. Take it with you whenever you go practice. Shoot it 2-3 times and put it up. It will last a long time.