Re: Remington 700 308 heavy barrel
If you're set on a barrel, give Jim Briggs of Northland Shooters Supply a call. He stocks Pre-Fit Remington barrels that utilize a savage-style barrel nut (the horror!). These are now being made by Criterion (division of Krieger). For about $300 total, he'll set you up with the barrel of length and contour you want, in stainless, along with a barrel nut to match. He will also recommend a thicker recoil lug while you're at it, and it'll be another $30 bucks or so. You will need a savage barrel nut wrench, and either a barrel vise or action wrench as well.
I bought one of his 26" Varmint in 6BR last year. They were manf by McGowan then. I couldn't be happier with it. Guess I got one of the good ones.
That being said, I believe you'd be further ahead to start by getting into handloading (if not already) and work up a great custom fit to your gun match load. look at 168 or 175gr matchkings, as they are a great value for the money, and fairly easy to get shooting well. Varget, RL15, or IMR4064 will be your friend powder wise.
Good glass that not only holds a zero, but has accurate and dependable adjustments is a must. Leupold, Bushnell Elite, Sightron SII and up... etc. And if you spend money on good glass, don't skimp on the rings and bases.
After reloading, and glass... then trigger. Shilen or Timney will drop right in and be good to go pretty much out of the box. It doesn't need to be ultra light, just consistent.
After all that, then i'd take a good look at the stock and bedding. And finally, after all that... then the barrel. Honestly, thats the order I'd approach it, and I think where you'd get the most bang for your buck. You can never go wrong with a quality barrel, but unless your factory remington has a very high round count, or damage from neglect or abuse, I think you may be shocked to see how good it will do for you at the ranges you have listed.
Good luck with the project! I'm a big fan of making a rifle "custom" to you, no matter the path you decide to take.