Greatest fun on Earth you can do while vertical is to build one like you mention. I use Remington 700, 40X, and 783 actions, along with the Savage single Shot Precision Target Actions.

My favorite barrels are the Pac-Nor Super Match Stainless Steel, with the Rem Nut for the Remington. I usually order Pac-Nor's polygonal rifling as I have found it extremely accurate in every caliber, and easy to clean. I use a twist calculator to match the twist rate to the particular bullets being used.

I rebarreled a 783 to .25-06 using one of the Criterion barrels from Northland Shooters Supply, and found it to be an accurate and well finished barrel. However, the Pac-Nor is superior, but more expensive with a longer wait time. Shilen barrels are another good choice, I have them on several rifles.

The last Remington 700 I did on a new Brownell's action. Like you I had it modified, except for the barrel threads. The best things I had done was to have the bolt raceway reamed, and the bolt double sleeved, to keep the top locking lug in contact with the receiver during the firing cycle. The lugs were fitted and the firing pin hole bushed, and a double pinned precision recoil lug installed, facilitating swapping barrels. I had the Jewel trigger I had installed timed. This was overkill, but it's a hobby.

The barrel nut does not detract from accuracy when carefully installed. I use headspace gauges to ensure that each barrel is within specs, and can be reinstalled exactly the same. I also use a Teflon anti-seize on the barrel, receiver and nut threads, to protect the steel and allow for consistent torquing of the nut.

Here's a couple of photos of what they look like:

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Above: Remington 700, Pac-Nor 24" Super Match .308 Winchester polygonal rifled 1:10" twist, Sendaro contour barrel, with 12 degree muzzle crown, Vais Muzzle Brake, Rem-Nut. Bell & Carlson Medalist M-4 Stock with Wyatt Outdoor detachable magazine bottom metal. OEM internal magazine and bottom metal is interchangeable. This rifle also has a Pac-Nor barrel in .22-250 Ackley that interchanges and uses the same magazines.


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Above: Remington 783 with Rem/Age Criterion barrel in .25-06, with .250" precision recoil lug, Boyds laminated stock. I still have to finish developing loads for this rifle. The Factory .30-06 barrel is shown on the table.

It's not a mistake to build your own, especially given that the .308 Winchester configuration shoots well under .5" at 100 yards for 10 shots.