Default "Cause code: Addr.Vcnt., 0" on all outgoing SMSes

After taking the KitKat OTA, I've noticed that every SMS I've sent has "Cause code: Addr.Vcnt., 0" in the Message Details (using the stock Messaging app). In addition, some people have reported extreme delays in receiving those messages, and MMSes have apparently not arrived at all (although that last one is speculative; nobody has replied to any of my MMSes despite them containing photos that typically get amused responses).

I haven't tried a different SMS client yet. The stock one does have a Delivery Reports toggle in the settings, so I enabled it; the cause code remains (but I am seeing a delivery confirmation mark on my outgoings). I'm not sure if the sporadic sending still occurs.

(Note: while I did have a few failed sends under Jellybean, they were few-and-far between. They also definitely didn't display a status message like this.)

A Google search turned up some dead threads on other sites, and some people who couldn't seem to send SMSes at all - but nothing that quite matches this.

Any ideas, or similar experiences?
Active Devices:
Motorola Droid Razr M (Verizon, XT907) (Rooted stock 4.4, occasionally testing CM 11 nightlies)
Samsung Galaxy Nexus (Verizon/"toro") (Paranoid Android 4.45)
Acer Iconia Tab A200 (Omnirom 4.2.2 unofficial)

Older Devices:
Motorola Droid X2 (Eclipse 2.3)
HTC Droid Incredible (Cyanogenmod 7.2)