Sounds about right. If I could find a Kimber in 338 fed I’d be all over it. The Kimber Adirondack in 7-08 is tempting but I’m limited in projectiles.
The Adirondack also comes in .308. That splits the difference and you have some good projectile options - even without the fact that you reload, there are factory loads for the .308 going all the way up 220 grain.
You strike me as someone that wants to invest a bit of time (and the money that comes with it) - in order to get a rifle that you are completely happy with. Based on that, here's a thought. If a larger bore is a must-have, then you can buy the rifle you actually want (regardless of the barrel that happens to be on it). Then take it to a smith and have him put on a new barrel in .338 Federal or .358 Winchester. Just bear in mind that a larger bore diameter will mean more material in the barrel - so for a given barrel profile, the barrel will weigh more.
Weight seems to be rather important to you. In my mind that speaks of someone that expects to carry their rifle quite a bit...and lines up with my line of thinking too. If weight is a priority, the Kimber looks even better.
Even without taking the gel out of the stock, that will give you very good performance and you will be well under 7 pounds even after adding a scope, rings, and a sling. Here's my thoughts on the math.
Kimber Adirondack .308 4 lb / 13 oz
Leupold FX-II Ultralight scope 0 lb / 6.5 oz
Talley rings for Kimber model 84M - 1" low 0 lb / 4 oz
Quality 1" Rhodesian or ching sling with hardware - 0 lb / 12 oz
4 rounds of .308 @ 0.85 oz each - 0lb / 3.4 oz
Total weight - 6 pounds, 7 ounces when loaded
To be honest, the weight for the Talley rings is probably at least an ounce heavy, since they only list one weight for the entire list of rings for that rifle - from 1" extra low to 30mm extra high. If you get aluminum rings, you can probably whittle that down even more...but since there is no backup sighting system, perhaps the solid steel rings aren't a bad idea either.
If you don't like the fixed power scope, you can take a (large price) jump up to something like the VX-6HD 1-6x24mm, a Swarovski Z6 1-6x24, or a Kahles K16i 1-6X24. Those three are all similar in weight, and would add +/-10 ounces over the fixed power scope. That would nudge you up 1 ounce over your 7 pound goal. I personally think that the 1-6 options are more scope that you'll ever need when engaging targets that are inside 200 yards - but my eyes are not your eyes, and my shooting experience is not your shooting experience...so scope your new rifle in the way that makes sense to you.
I would only have two concerns about a Kimber set up in that way - and both of them are definitely YMMV points that are based on my own experiences and preferences.. First is that the length of pull is about an inch and a half longer than I prefer for a rifle being used in relatively close country. The second is that it doesn't have any iron sights.