Are there Precision, Longrange Capable rifles out there, these days (I have not kept up)? Rifles that do it all and weigh next to nothing? Great Glass scopes that work on a lightweight system, are under 10oz, and have all the features and resolution? Are there spiral fluted heavy varmint barrels that do it all but weigh around 2lbs?
I can think of a couple of factory, production line rifles capable of stellar performance, IF the operator is a precision handloader; but only a few. Sako TRG-42, whatever magnum Accuracy Intl is making these days, Maybe a SIG match bolt rifle. Used to be the Winchester USRAC Marksman made at their custom shop with Schneider barrel and McMillan stock. The FN-Herstal Police rifle in .300wsm is an option if shorty magnum works for your application... Lots of custom shops out there doing LR guns, but not usually with inventory ready to go. Maybe H-S Precision? McMillan Rifles, Barret, Brown? Tons of newbies that opened shops since about 2005, but how many got guns ready in inventory to sell just like you expect it to be outfitted?
If you're cool with the lack of a pin block in your Remington bolt, ie no real safety, then get with the program and go custom barrel for your 700 and maybe do a better stock. If you don't handload, time to learn. Buy a Schmidt & Bender scope and quality mount system and eliminate all the variables.
There's not really any "factory solutions" for under $4K for a decent rifle and about the same for your optic system. Buy a used Sako and rebarrel with Krieger and be done with it... AI has their rebarreling down to a system, worth the money; if you got it. Makes AI very unique and at the top of the game.
Of course, there's always the AR-10 world for precision. The AR-10 is a real alternative, but it don't appeal to the purists. Too bad, they work really well and some of the best custom shops out there make uppers that are first rate excellent.
Learn to load match quality ammunition and you'll be on the road to precision shooting...