What you're looking for does sound a lot like a Scout rifle - so a Ruger Gunsite Scout or a Steyr Scout might not be a bad choice. Both are exceptionally handy and quick when fitted with the right optic (1.5-5X Leupold VX-R or 2.5X Leupold FX-II). Once you learn how to use a Scout scope effectively, it's as fast on target as a red dot and offers definite advantages over a red dot as the range opens a little bit. I know that the tupperware stock on the Ruger doesn't feel great - but since it's almost a pound lighter than the laminate stock, it makes a lot of sense for a rifle that gets carried a lot. I've put more meat in the freezer with my tupperware stocked Ruger than with anything else I own, and most of that was taken at less than 100 yards. If you don't mind the weight, the laminate stock is attractive and still handles very well with the short LOP.
For cartridge selection, .308 is effective, easy to find, and relatively cheap. If you are rolling your own, Barnes makes a great little 168 grain copper pill that has served me very well - enough so that I'd be comfortable using it in the vast majority of hunting and predator defense situations. It's also very easy to load so that it's ballistics mimic those of the 168 grain Federal pill, so you're not slinging expensive monolithics down the range when practicing. (and you already know enough to verify your zero again with your hunting load before venturing out to fill a tag). That sort of load also has the advantage of shooting relatively flat, so I've found that a 200 yard zero (and 225 yard MPBR) works very well for what you actually encounter in the field. If for some reason you find yourself needing to push out further, you've only got 8 inches of drop at 300, so even a small amount of practice at that range will mean that even if you don't have a fancy or exotic cartridge that all the gun scribblers are loving you'll be able to fill the freezer.
If you like the idea of a larger diameter projectile, the .358 Winchester is a logical step up - since stepping up to a longer action and a .35 Whelen seems to represent more horsepower than you're talking about wanting. If you want a true thumper in a light and quick handling package, you could look for a Steyr in .376 - but that is most definitely not a rifle for someone who objects to recoil, and I'm told that there are only about 300 of them.
If the Scout concept isn't quite your thing (and there's a definite learning curve associated with forward mounted scopes) then I think that your original concept with the Kimber you own is very sound. A Kimber Adirondack in .308 will be very light, handy and quick - 18" barrel, and under 5 pounds. If you put a low-magnification scope on it, I think you'll be very happy with the results. For the ranges you're describing a 2.5 X fixed power will absolutely get the job done - or a 1-4X would work just fine. The advantage of a fixed power scope is that you'll end up with something that is lighter, simpler, more rugged, and with better clarity than a variable power scope in the same price bracket.