You can leave Vietnam if you've already submitted your application. Plenty of people have already done what you're asking. It's UNREASONABLE for you to be expected to remain in Vietnam when you don't know how long your application will take to process. Just leave, and then reenter Thailand when the DTV is approved.
OK, but I would still prefer to take a quick trip to Malaysia than to go to the Immigration Department 3 times because apparently my papers are not enough for them. To each their own. I'm not doing that stupid extension process.