I agree with the above, I would try different loads, and different bullets, till you find what the rifle realty like at distance, just cause one likes things close does;'t mean they like it far out there seem this many many time over the yrs!
I also would eb inspecting all things too, bedding, trigger, scope mounts and even barrel crown
I would also be using a chronograph your shot strings and see if there is any correlation to ones that go of and the speeds in them as to those that group better!
if your reloading and I have NO clue your experience lever
what are your steps in doing so
how picky are you getting on things, you weighting every charge, every head, every CASE, are you sorting brass out by case weight?
how about primer pockets?
when you get real serious about long range shooting its a LOT of the small details that make the difference, in both tight groups and or misses and larger groups!
I dont' think I would be waiting 15-20 minutes between shot strings either, your getting more cold barrel like start ups
I would do strings of 5 or 6 shots, then cool down and repeat(well pending air temp that is, if your firing away in 90's or higher, , this alone might be the issue?
I also am NOT a fan of lead sleds at all for accuracy !
learn good form, and breathing and some GOOD rest, and that is all one should need to do so
if recoil bothers you(and take with a grain of salt no offence meant), maybe you should be using a smaller caliber?, be adding a muzzle brake or like option to tame some to your liking better!
I have 30+ yrs of shooting 1,000 yards with 30 cal and larger in matches and thousands of rounds in practice and for fun!
recoil doesn't bother me me till I get into some real big bores and then still need a bunch of rounds to get me(owed a few .50 BMG bolt actions and semi shoulder rifles too LOL
so I get recoil, and to some it does effect them a LOT more than others