Marriage with Marriage certficate = legaly married
Marriage without Marriage certificate = not legaly married
How would you defend your case without legal papers. Remember that most U.S Government agencies like the Department of State and the USCIS works in a beucratic system. Everything has to be written, legalized, according to procedure, etc.
I hope all the best with your process. It might feel like there is no hope for getting that Green Card but then again, it is not for us to decide. They might be still hope. I would recommend consult an immigration lawyer that understand this kind of situation. If you said that common law marriage is common in Texas, then consult with a professional in State of Texas that know how to handle this situation. Understand that there is a difference of laws in the U.S. There is State laws and Federal laws. Common law marriage might be legal in Texas because of their State laws but might not be legal in the eye of Federal Government. A good example is gay marriage in California. It is legal in California but when you get out of the State of California or even go to the Federal government level, the marriage is not legal anymore. DoS and USCIS works under Federal Law.
You still have plenty of time to find a solution so you can defend your argument at the interview. If you truly want that Green Card, try as hard as you can to find a way. At least whatever happened after the interview next year, you know that you have tried your best.
Good Luck!