Well, now my phone is rebooting like mad. Over the past week I had a few post-update reboots, which were annoying but still pretty consistent with the intermittent rebooting I had before.
It got worse yesterday, and today, the phone is just going nuts - in rebooting loops randomly all day. Basically no rhyme or reason that I can tell - it can be on the charger or not, have a full battery or low battery, I can be using an app, or the browser, or the phone, or doing nothing. No new apps installed recently, and I've always had a good signal in my house.
I even did a factory reset and wiped everything, even though I couldn't see how that would have any effect. It rebooted several times after that (and I had NO apps installed at that point other than the preinstalled stuff).
I got my DInc in June and was really happy with it up to this point. Heading to the Verizon store tomorrow to request a replacement.

Hope that (1) they don't give me a hard time (2) I don't have to wait too long for a new one and (3) my new one works!