Awesome thread. I began reading yesterday, and eventually started skimming through it, and just finished today. Obviously I am not getting any of my own work done. HAHA. Great story. And congrats.
My thoughts on your space problem: Don't do a damn thing. The original Sonny Bryan's here in Dallas is similar to that. It's packed and they sell out when they sell out and there is no room to park or eat inside. People eat on their cars in the lot. If you want it as a consumer, you plan accordingly. And people do every single day for as long as I can remember.
You said your business model was to see far fewer daily visits than you are seeing now, so this must mean you are profitable given that you are 2-3x greater on daily visits than anticipated. That being said, people will adapt to your routine. You have been open only a few months. As word spreads, people will line up far in advance knowing that you will be sold out and if they want a spot in the parking lot, they are going to have to get their early. Seems simple enough. BBQ is a very time consuming business and as the man in charge of doing it all, if you try to please everyone, you will run yourself ragged.
Just my opinion.
I'd sure like to try some of that spicy sauce!