Shorter barrels
I would not go less than 20 inches, but would probably cut it to 22 inches. The two extra inches will not make much difference in handling, If you are hunting the black timber, where shots tend to be less than 100 yards, a shorter barrel is the way to go.
When Remington first came out with the 700 in 1962, all their barrels were 20 inch barrels. The quickly changed in 1963, because the standard was 22 or 24 inches, and from then on, sales picked up quickly.
I still have an original 1963 Remington 700 in .308 Winchester calibre, and a low four digit serial number. To me, it is almost the perfect rifle for my style of hunting big game animals under 300 yards. If you have hunted a lot, you will have to admit that 85% of your Big Game was shot under 200 yards and most of these under 100. And that is over 50 years of experience, most of it in the mountains of B.C.
I am glad to see that you want to keep the open sights. A lot of people remove them when they get a rifle, but the smarter hunters fire some rounds to zero the open sights, then they can mount a scope on the rifle. Sooner or later, there will be a scope problem, and Murphy's Law states that it will be in the middle of your hunt. With open sights, you can still carry on.
In one of the most amusing TV hunting shows I watched, the Hunter came to northern Manitoba for Moose, and his scope got banged up and was useless. No open sights on the rifle! No spare scope! He then had to resort to a bow and arrow, and lost his moose because it was about 60 yards away, and not really in Bowhunting range.
Your front sight should not be too much of a problem. If it is the band type, a steel mandrel that is the size of your new barrel diameter can be turned on the lathe. You can heat the band, and drive the sight onto the mandrel, (or the mandrel onto the sight,) to increase the inside diameter of the band. You will have to re-blue or refinish your front sight band, but that should be no problem. If that is not feasible, then get some tubing that will fit over the cut barrel snugly, and cut the band, stretch it a bit, and silver solder it onto the tubing while silver soldering the front sight on. File to smoothness, and blue it.
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