Since your feed failures occur when the magazine spring is under greater compression (nearer to full), the extra friction this creates with the magazine lips is apparently being the straw that breaks the camel's back, not the shape of your chamber or feed ramp. It is possible that just using a different magazine will fix the problem, or that polishing your magazine lips will fix it. An experienced 1911 smith can check that their shape is correct.
It is also possible, however, that your recoil spring is a little stiff and the loads aren't getting the slide all the way to the rear. The fact this got worse in the cold, when the powder is likely to burn with a little less vigor indcates this. However, it could also indicate you are using a lube that gets stiff in the cold. It could also indicate that your grip is too loose on the gun. Use a light oil. Try a Weaver hold or sandbagging so your body is more immobile behind the gun and see if that matters?
If none of the above works, and especially if +P loads cycle fine, then you may need your recoil spring lightened a little. You are, as Harry said, getting into something best for an experienced gunsmith to do. A general reliability package is a more-than-slightly worthwhile thing to have done on a carry gun anyway.
By the way, the "hastle" of sending it back to Kimber are likely a lot less than you think. It is legal to return a gun to the factory directly, and for them to return it to you directly. No FFL transfer is required, but check the carrier's rules whenyou choose one. Send it by 3rd day air, but don't send it by ground. That reduces the number of hands it passes through from about 100 to about a half dozen. I have had terrific good luck with returning guns to their factories for work. In my case it has always been accuracy complaints and they have always come back shooting really well, and the work itself has always been free of charge. Getting the relibility package is still a good idea for carry, though, and the factory isn't going to do that for free. If they offer it at all, it will be through their custom shop.
Nick