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First, a warm welcome to HuntChat.
The easy one first: Remington is the only maker of 7-08 brass that I know of. It's in current production so any good store or catalog should list it.
Now to the other question. Necking brass down does thicken the necks simply because the brass has to go somewhere. Outside neck turning is generally better, especially if the brass is thicker on one side than the other (which is more common than having it equal). Inside reaming will remove brass, but the reamer will simply ride the off-center hole, leaving you with thinner but still off-center necks.
Now the better news. For most factory rifles, you probably won't need to ream OR turn. Factory rifle chambers are pretty generous, and having a slightly thicker neck might even improve the cartridge fit.
Neck one .308 case down, seat a bullet in the empty, unprimed case and see if it will chamber easily. If you have a good caliper or micrometer, measure the diameter of a fired and unsized cases versus the dummy round with the bullet seated. If the dummy round is .002" smaller or less, you need to turn cases a bit. If it's .004" smaller, you're good to go.
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