Well, after an hour long online chat with a very helpful Sony rep, I'll be returning my Vita for service/replacement to Sony.
Multiple Database Rebuilds and system formats later, I was still getting the same error, even on a clean system. Turns out it's apparently a hardware issue.
I'll update this thread after I go through the whole packing it up and waiting for my Vita to come back to me with how the Vita return process goes.
Update number 1: I submitted my RMA request on Sunday and received the box from Sony yesterday (Tuesday) morning. I packed up my Vita (after removing my cards, deactivating my account and formatting the system, as instructed), and shipped it off yesterday afternoon. Sony received my Vita and accepted my service request this morning (Wednesday) and will send me another email when my system is shipped back to me. Typical turn-around is one to two days, according to the email I received.
One of the advantages of living 90 miles from SCEA in Fort Wayne, I guess. Looks like I might have my Vita back by the weekend.
Edit to add: Not a single phone call has been made on this case. The Sony rep set up the RMA through the online chat system on the support page.
Update number 2 (and final): Got my PSVita back today (would have had it yesterday if I was home when FedEx tried to deliver it), and I did not receive my own PSVita back. I received a replacement (as I suspected I would). I can't tell if it is a refurb or a brand new one, though. It was wrapped in the same padded sleeve that brand new ones do, but it was packaged in an unlabeled (other than the shipping label) box. All of the buttons (including the oft-complained about L button) and both sticks are nice and tight, as if it were brand new. Immediately upon finishing the initial setup, I was informed that a firmware update was available (it shipped with 2.02).
All in all, a very quick and satisfactory experience. Thank you SCEA.