The 300 WSM is a great cartridge. The 8400 is an excellent rifle. I own a Kimber 8400 Select Grade in .338 Win Mag. I love its looks. I have been able to get 1 inch groups with hand loaded 180g Nosler AccuBonds but larger bullets like the 200, 225 and 250g bullets do spread out to as far as 1.25 to 1.75 inches at 100 yards as bullet weight increases. The 250g AccuBond in .338 can kill almost equally as well, a Cape Buff as a 300g .375 H & H Magnum as the point blank energy is virtually identical at 4000 ft-lbs but can kill a Muley Buck with 180g heads at 500 yards shooting MOA 180g heads. The shooter has the most built in error at that range with adrenaline, poor rests, lack of practice at that range. How good are you? Scope? Magnification? Bench rest gear etc.
The 8400 rifle is lighter than most and the barrel is pencil thin so carrying less weight is a reason to buy if you are a mountain hunter or one who is carrying all day long.
I was, like you, initially disappointed for the dollar spent in getting worse than MOA for the heavier bullets. And not even sub MOA for any hand loaded bullet.
It is important to note that most new rifles will improve in accuracy over time and need more than 100 rounds shot to accurize a rifle. Cleaning and shooting after each session is essential. I would Google Breaking in a new rifle to see techniques you might use on your Kimber.
Dwight Van Brunt says that because the barrel is thinner you will have to let the barrel cool between shots and my barrel does heat up fast so he says first shots count more in accuracy.
No question my 8400 is very beautiful but it does not appear to perform at a sub moa level when repeat shots are taken with my caliber and limited experience with the 8400. Bull barrels on other rifle brands absorb heat and deliver more accuracy but are heavy as heck to tote in the high mountains. My sons Savage Model 10 in .308 Winchester, heavy as heck bull barrel with an accutrigger shoots 3/4 to 7/8 groups with 140g Sierra HP hand-loads but is not in the same league at all for delivered energy. Too heavy for deer hunting all day in the field.
That said, you can spend more money and get guaranteed sub-MOA on the same kind of 8400 weight gun and get really good performance as guaranteed sub-MOA three shot groups. I have found that the simms vibration laboratory barrel dampener does reduce group size by a sizable margin on my 8400 with 200g Nosler e-tips from 1.5 inches to 1 1/8 inches.
I will say this on rifle accuracy, when you find a rifle that shoots sub-MOA groups for most of the ammo you shoot, then treat it like gold. I have a Ruger M77 Hawkeye African in .375 Ruger that shoots 260 grain Nosler AccuBond bullets in 5/8 inch groups at full power loads at 100 yards. I have to load down for deer and accuracy changes little. I am afraid there is no equal to this rifle without giant dollars being spent.