I have a Lumia 920 on AT&T, and am not familiar with your issue, perhaps it is just a Verizon thing. That said, AT&T has their issues too, primarily as they have not rolled out the Amber update with GDR2 yet, nor have they even issued a release date. I finally gave up and flashed the ROM on my phone to unbrand it, which immediately allowed the Amber/GDR2 update to occur. My phone works much better now (no text issues that are discussed in this thread), but my wife and kids were afraid to flash their phones (voids the AT&T warranty, and there is a small risk of bricking the phone), so they're still waiting for their updates; and when they do receive the update, AT&T will have removed the Data Sense app, which is a really valuable part of the update (I have been considering switching to Verizon, do they strip out Data Sense?)
Concerning the Verizon text problem after GDR2, take a look in the Access Point app (under Settings), and see if you have multiple Verizon connection options (I see 3 different AT&T options with mine: 3G, LTE1 and LTE2), so perhaps it would be worth trying a different Access Point to see if that might fix the problem. If not, or if you lose all connectivity, just switch back to the current setting.
Good luck,
Andy
