Good new, then some bad news.
Good news, when I bought the first Kimber Stainless II, I bought two of them. I ended up transferring one to little brother. The problem 10mm is actually the third one I bought. The good news is, I have it here for evaluation as it has never been fired.
It is pretty smooth much like the 45 version I have. Cleaned, oiled and ran 150 rounds through it. It ejected every time. The bad news is, it didn't run a single mag without chambering issues. 1-3 per mag. Usually 1 or 2. 50% of the time the last round would get stuck.
In reviewing what was going on, I observed that the nose was in the chamber every time. In my mind that really left 3 things I could think of that could cause the issue, 1 not enough energy/momentum to push the round through (like the Springfield), 2 the chamber was too tight/sharp to make the turn, 3 the rim isn't getting behind the extractor when stripped from the mag.
I don't think its an energy/momentum issue. A light tap on the back of the slide will usually will send the round home. It only did so three times. I am not good enough to diagnose a tight chamber. Which brings me to the third possibility, the rim isn't getting behind the extractor. At least for the most part, I think this may be the issue. looking at it in the pics, it appears the rear of the round is pushed to the side.
You can't really see it in that picture but the rear of the round is slightly depressed into the mag as well. If I pull the slide back just a little bit to take the tension off the round, the rear of the round will pop up and align with the chamber. If I let go of the slide from there, it will push the round in on its own. Its important to note that when I do that, the rim is now in front of the extractor, not behind the hook.
Here is another view. From here, it looks like the rim isn't clearing the extractor.
In addition to the chambering issues, there was one instance at the end where the slide locked open before chambering the last round. It was a partial slide stop engagement like the previous 10mm but I noticed that in this instance, the round was already pushed all the way up to the feed ramp. I believe this was due to the round above it pushing down on it in an unnatural way due to being pressed down by the extractor and possibly caused the round above to drag the round below it forward. It is possible that the follower moved far enough up that it started to engage the stop. I don't believe it is the same as the previous 10mm. If you look at those pics, the round is seated to the rear of the mag where it belongs. I think this is a case of the same symptom, but different cause.