I'm not a fan of light weight, long range rifles. But, some people report good results.
A factory generation 1 Sendero 7mm Rem Mag with a 1:9.25 twist will do everything you want.
Whatever you do, get the best optics and electronics you can afford. A good NF scope on a factory Sendero will likely be better than a custom rifle with a mediocre scope.
I like the Leica 1200 CRF. But, there are some more current choices worth consideration.
Good software on a PDA with a manual backup plan will be essential.
If you have all of that covered, then anything you can do to improve will be gravy.
You should start with a trustworthy smith. There are several in these forums that I wouldn't hesitate to use.
Finding the right barrel without a 6-9 mo wait can be a challenge. I like Kreiger and Bartlein with a 1:9" twist. My recommendation would be for nothing less than a light Palma contour. But, that'll blow your weight budget.
Also, the more overbore your cartridge choice, the longer the barrel needs to be to take advantage. Hence, more weight.
A Stiller TAC300, Lawton, or similar action won't cost you much more by the time you pay for a Rem 700 to be blueprinted.
You might want to consider 7STW for a little more punch at the expense of barrel life and longer/heavier barrel.
I would definitely go with a brake so that you'll enjoy practicing. Holland QD, Muscle brake, and Painkiller are my top picks although, I've only used the QD. You can have your smith make a thread protector if you want to shoot sometimes without the brake.
Consider EGW HD or Nightforce 20MOA picatinny rail with Burris extreme tactical rings.
I like Timney triggers. I have not tried Jewell, but they are highly acclaimed.
I like Manners and HS stocks. They are solid but heavy. I beleive the XLR chassis (XLR Industries | evolution
) might be lighter weight with a few nice features.
I have a featherweight stock for Win M70 LA that's very solid that I would part with. I know it's top quality, McMillan, B&C, etc. I just don't know which for sure since it came on a custom rifle that I've since rebarreld with a Kreiger palma contour.
Hogue is another option for a good stock that's not too heavy. I have one with the full length bedding block on my Mauser 98 and really like it. These are much improved over the Hogue stocks that Rem sticks on factory rifles.
Hope this helps. Let us know what you end up with.