I have an update.
After giving up and going back to JB last year, I've been using my phone religiously with acceptable results. Rooted, Tether, Texting. All working well. I just didn't have some of the nicer features of the newer OSs.
Last week, my power button gave out. So VZW sent me another phone yesterday. I had to return my old phone to stock, so I flashed a different ROM on it in anticipation of the new phone coming and unrooting the old one.
I stuck KitKat on it. And somehow, texting was working. I couldn't believe it. I thought the issue was gone. So I put it back to stock, locked it, and S-ON. It's going back tomorrow.
I started shoving ROMs onto the new phone. I really just want GPE. Turns out, that's not gonna happen. The SMS issue is still there. I tried a few different ROMs to no avail. Finally, I decided to try the ROM I used on the old phone., and it worked. I'm using dlx-kitkat_Full-Odex_4.09.605.1_CL322791, and not having a problem so far. Now, I don't know if I'll be able to tether with this. I'm hoping there is a tether solution for Kit Kat because that's really how I primarily use my phone on the road. But for now, the stars have semi-aligned and things are working almost as expected.
I hope this helps someone.
EDIT: A few hours later and still going strong! I wish it weren't a Sense ROM, but I'll make do.