How can I stove-cook meals for groups of 6-8 with only one burner?
Generally, it is said that you should avoid pans which are not the same size as the burner. You are wasting energy in both the "smaller" and "bigger" case. Besides, as Jessica mentioned, you are wasting time and getting lower quality food with a larger pan, because you have to stir a lot, and still get unevenly heated food. 

But if the alternative is to cook two batches in a fitting pan, I still think that you are saving electricity and time with the inefficient large pan. So I would stay with it. 

I can also recommend buying more burners and an oven, if you are going to cook. A portable burner is very small and can be stuffed into a cabinet when not needed, to save counter space even in the tiniest kitchen. It can be cheap, or you can get an induction one for better quality heating and energy saving. A toaster oven is, in my experience, much more useful than a microwave. This will depend on the way you eat - if you frequently get frozen meals, the microwave is more convenient. I do all of my normal baking if a toaster oven, and it does everything, even complicated cakes, so if you are serious about cooking, it might be a better use of space than the mw.