Nope, not in the outback just yet....but sooooon.
(Upcoming week long rat trip with the crew.)
Well then, it appears you are already an accomplished rifleman, so my suggestions may already have been addressed. The 7-08 is an inherently accurate cartridge, so the problem most likely lies with the rifle as you surmise. (My light/mountain rifle is a Ti M700 clone 7-08 Ackley and shoots bugholes. It's an elk and mulie killer of the First Order).
You seem to have done most common loading tricks, but have you tried different seating depths with your favored bullet?
Have you checked your loads for concentricity with a dial indicator?
Here are some additional points to address:
* Have you checked the bedding?
* Does the stock touch the barrel at any point?
* Has the recoil lug been bedded properly? Meaning it only
touches the recoil lug mortise at the rear only, and not
the bottom or front?
* Is the first 2" of barrel under the chamber area properly supported?
* If you have a bore scope, you've already checked the bore for irregularities, but if not, it's something to check.
* Have you checked the crown under magnification, and the last 2" of rifling at the muzzle? Is the throat is good condition?
* No chance of the scope base screws being too long and touching the bolt? (Seen this one a lot)
* Do the lugs bear evenly? Have they been lapped?
I had a Kimber rifle that always seemed to 'smoke' cases, even with heavy loads. Sent it to the Mothership and they did a chamber cast and found the issue. Fixed it and returned the rifle at N/C. Not really sure what they did either, but the problem disappeared once back home. Sometimes the Mothership performs unnoticed miracles that we mere mortals don't seem to understand.
If all this is addressed and the problem still persists, then it's most likely time for the rifle to take a factory trip back home to sort it out.
Sorry I can't be of more help, but without the rifle in my hands, I'm really just guessing with the most probable causes that I've seen over my lifetime with problem rifles. I wish you the very best sorting the issue out, as the Kimber rifles are indeed sweet shooters.....most of the time. The rock chucks here fear my 84M Varmint 204!