Sorry to hear you are having a problem with your Savage.
I have a Savage 10FP (hidden mag) and one of my buddies has a 10 FCP (detachable mag) and my son and another buddy have 10 FCP-K with the detachable mag and the muzzle brake.
All these rifles chambers will easily take a 2.820 168 SMK and the nominal specs for them are 2.800.
I load Noslers out at 2.830 in mine without a problem and I am still more than 0.050 off the rifling. The only limit on seating depth with the mag fed models is the internal length of the magazine. My hidden mag is actually a bit longer than the detachable versions.
If you still haven't gotten to the bottom of your problem, I would call Savage and talk to them.
It sounds like they might have set the barrel a turn too deep into the receiver.
It doesn't take much to eat up 0.1 inches or more in final seating. Your chamber seems to be less than 0.1 inch from what I would have expected it to be, but it also seems like it is more shallow than it should be.
Savage has a really responsive customer service group.
My buddy with the new 10 FCP-K was having trouble with the scope mounting screws. His scopes were way off to the right (8 inches at 25 yards).
After trying two different scopes and three sets of mounts, he called Savage and they had him sent it back to them. They tested it and sent him a new rifle because they could see it wasn't right. Because it would have taken quite a while to refit it, they just gave him a new one and took his rifle through the quality control process to see if the misaligned mounting holes might have resulted from a manufacturing problem.