Producer positions are fairly rare, and when they show up they demand industry experience. Right now Gamasutra's job board has 11 job entries under the producer umbrella (compared to 88 programmers and 45 art related jobs). One says "associate production manager" and lists a strict requirement of 3 years of industry experience. The others I glanced at were all 5+ years of industry experience.
QA is a possible route in, but the odds of you working a QA job over to a producer job is not very realistic. Sure there are tales of janitors becoming CEOs, but that isn't a good plan. I have known hundreds of people who worked in QA. Most worked through a 3-month or 6-month contract and were never seen again. I know roughly five who moved into other roles, usually low-level designers and one as a concept artist. My observation would be about a 0.5% chance of just converting the job into a permanent position at all. Not good odds.
Your internship with the game company and with restaurant management is probably the best lead you've got. Don't waste your time with a QA job. Are you close enough to that same studio that you could work there? Dallas has game companies, and so does Austin, so don't let that stop you. Do you still have contacts with any of those individuals? If not, fix that and re-connect.
Personal connections are usually the best bet for this type of job. Look for the friend of a friend of a friend who knows somebody at a game studio, and become their new best friend. Talk to them, and figure out how to help them make a position for you an associate producer.
As you talk to those friends-of-friends, you will need to leverage your prior experience quite a lot. Here are some things I would think about in trying to make the transfer:
Producers rely on calendars and emails; they are much like the restaurant manager who keeps everything running smoothly. Producers need experience so they know when things are going to happen and how to guide them. My best producers that I have worked with have been more like security guards around the development team -- they invest incredible amounts of energy to ensure the developers can spend time developing. They make the schedule work, although I honestly have no clue how. If someone even starts to approach an artist or animator or programmer with any problem not directly related to the task at hand a good producer will (proverbially) tackle that individual to the ground and prevent them from disturbing anybody. They do everything they can to block interruptions, dealing with the person and getting the material on a calendar instead, and gently introducing whatever it is to the team at the proper place in the schedule. Like the store manager, you need to keep shooing the teenager's friends away, handle all the complaints, and deal with every emergency preferably before it becomes an emergency. You need to fill in schedule gaps and timing issues as they appear, hire and deal with contractors, and do thousands of other things around the studio.
You already have connections from working a year as an intern. You already have management experience in the food industry. Do you want the job or not? Don't wait around trying to win a lottery at a publicly-announced entry-level opening. You need to intelligently navigate your social network and actively knock down the barriers with tact and diplomacy, politely yet firmly getting people to see that they need you. It will be good practice, because that is most of what a producer does daily.
: Typos are fun.