I remember back when Jeff Cooper was writing about his scout rifle idea in his G&A column. At the time I thought it was a good idea, but I almost certainly had a different idea of how it would be since my experience was vastly different than Jeff's. For me, I imagined it as a short-barrel, large bore, 30 to 200 yard range rifle with a forward-mounted, long-eye relief optic with a wide field of view and good low-light performance. You've got to remember that back then, red-dots, holographic and other reflex sights weren't generally available. Nowadays, we'd probably spec one of those types of reflex sights with an optional magnifier. But I think there's also merit in refractor scopes that will go down to 1X. Back in the day, the best I found was 1.5X.
Jeff's idea was bolt-action. Today, there's a lot of very good and affordable AR10 actions that weren't really on the market at that time. Of course they existed, but the market was totally different. Back in the day, I explored the idea using a Model 70 and a Mauser 98 action. If I were to do it again, I'd start with a consideration of the caliber and weight I wanted. For a lighter gun to carry in the field, a T3X Lite could be a good starting point. The barrels are as short as 20" from the factory, and they can be cut down and crowned fairly easily or a muzzle device added. An AR10 platform is going to be heavier. It's also worth looking at the M1 action if weight isn't a primary concern. The Springfield SOCOM 16 and Scout models fit the role, but would easily break 10 pounds with some optics. Jeff's spec topped out at 7.7 lbs.
I wouldn't rule out a big-bore lever action like the Marlin 1895. They're short, and they have "tactical" models now with a rail. Add a wide field of view optic of your choice and they'd absolutely meet the scout rifle concept criteria with a shorter action than most any other. .45-70 won't deliver as much energy at long range, and the drop is significant, but to me the scout rifle idea was never for long range. But today we have more and more rifles built around cartridges designed for VLD bullets that can hold a lot of energy out to 1000 yards, even better than .308. The Scout rifle was never a precision rifle concept, but it was a "general purpose" rifle, and your idea of "general" might involve a broader range of purposes than what was conceivable in the 1980's.