Get ready for lots of folks to jump in, slide right down your throat and let you know how bad an idea that is.
For my part: It is completely unethical to contemplate field shots on game at those ranges. The vital zone on an antelope is not big enough for even 1MOA of minimum precision at that range and you risk wounding the animal and losing it. I wouldn't take that shot over 500yrds from a dead solid rest. It's not a target, it's an living animal and a public resource not to be squandered on silly pissing contests to see if you could get one that far away. If you can get within a mile you can get within 400yrds (which is still very very far for hunting) and take an at least borderline ethical shot.
All scopes add weight and you're asking for something I don't think exists, super light + high magnification and 1000yrds precision sort of capability. At 1000yrds I use a fixed 10x more than anything (or a 5" astronomical telescope and a webcam), below that sort of extreme range (well.. closer to under 600yrds) 3-9x is sufficient for most of my purposes. Beyond 1000yrds I start using 16x and hating it to bits. So much pulse bounce it's unreal. I have taken very long shots on game, in excess of 500yrds standing up and lucked out and killed it dead right there. That was too far and I was wrong to have done it regardless of outcome. It was so far outside of responsible I won't ever repeat the act, and you're thinking of twice that far.
Now to the technical matters: contour doesn't matter. Sporter weight is as good as heavy barrel for a 1-shot hunting gun. If you plan to shoot long strings at paper/steel then as heavy as you're wiling to carry, 8" twist for the heaviest bullets.
Personally I don't think you've thought this through. The biggest fastest laser beam isn't always the best killer.
flame suit on. (I can't wait for the anecdote spitters to join in so I'll get this out there in advance: Just because it happened once doesn't make it right!)
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