I'd like to update my results. From last night, just like djflan, I removed HD Widgets and so far, 7 hours later, the crashes are gone. So I have my fingers crossed that I've found my culprit.
Also, I installed the HoloWeb browser and I have found it to be quite a bit quicker and more stable than Chrome. For those of you have issues with Chrome it is worth a few moments to track this app down (here on XDA) and give it a try.
Some of you may not have remembered or gone through the Android 3.x transition, but these kinds of issues were very prevalent during that update as well. Many developers simply don't or can't test on a wide enough range of devices and OS combinations to catch all the issues, or they rely heavily on assumptions or code that "always worked fine" in the past. I think we're seeing the same sorts of behaviors again with 4.2, so it will take a couple of months for it all to shake out.
For now I think I have a stable configuration on the Nexus 10 and I'm sticking with the device. No RMAs will solve issues that are software related in my case.