I gave up and called Tech Support. Tech Support told me to do a Factory Reset. Result: The Bionic -- bless its little heart -- did the data drop thing while I was on the phone with the Tech Support guy immediately after the Reset.
Result: Tech Support Guy is shipping me a replacement phone.
I suggested to Tech Support Guy that he, oh, I don't know, READ THIS FORUM, because obviously I'm not the only one experiencing this, so sending me a replacement Bionic might not be the way to go.
Tech Support Guy said that the way the Verizon troubleshoot ladder works is: Phone first, network second. In other words, they have to send me a replacement phone and the replacement phone has to similarly fail before they will escalate to the step of considering the possibility that the problem is with them.
(It didn't help at all that Tech Support Guy himself has a Bionic which he says is working fine since the .905 update -- which is pretty much when mine went all to sh*t.)
ANYWAY, I feel like I'm "taking one for the team" by going through the step of replacement phone. I completely expect the replacement phone to ALSO drop data on a regular basis, at which point I eagerly await Verizon's promised escalation of this issue to the network level.
(Tech Support Guy also seemed to imply that we should be flooding them with replacement phone requests -- on the theory that "the more phones we send back to Motorola, the more information they'll have figure out the problem," if it is, in fact, unique to the Bionic.)
Excuse me while I go reinstall all my apps (thank you, factory reset) before I do it all again once the replacement arrives next week.