Thanks everyone for your suggestions. Just road-tested the Razr to do some troubleshooting, and predictably the Razr dropped the data connection as I proceeded from a densely packed area of Seattle to a remote area ~ 1 hr out of town.
The Razr then went into one of its hallmark fits and I could not get data back at all until manually switching the unit to CDMA only. Only then did I recover stable data (3G).
So the answer I think is that this is an issue both of coverage and of the phone. Verizon over-promotes the 4G service it provides; in my hands, coverage is quite sparse relative to 3G. This issue is compounded with the phone's inability to just switch over to 3G without going into settings to force the switch to CDMA, even with this update that was sent out recently supposedly to fix this problem.
Perhaps there are better phones out there that don't have this problem (but they are all probably buggy to some degree, I suppose).
I'll have to try the approach of cereal killer next and factory reset the phone, but for those readers having a similar pattern of difficulties, I hope this post is of use.