Answered my own question (mostly)
OK, I found out why this started happening. Somehow I had changed the setting in Google Voice, so that text messages were getting sent my cell phone. So duh.... when I received a text to my Google account, it also was going to my Verizon account, and thus my stock messaging app. I found this out when I saw all the text charges Verizon was billing me for. So now I am using that App, called Stock Messaging Application with Google Voice, It looks somewhat like the stock application- but not quite (I like the stock better). It does catch messages coming in from both Google and and Verizon. I have it set to reply to all through Google- which it does. This is mostly what I wanted to do- the problem is, it's a little buggy. Sometimes a message won't go in or out. And as I said, I still like the stock app better.
So I still have a remaining question. Does anyone know if, or when, the breakthrough of this from July (for Cyanogen Mod) is showing up for other ROMS?