An electric Skillet with a lid is the way to go.
Walmart has one on sale for $19.00. We have one that is 11" and fits on the kitchenette counter quite nicely. I think this is the best way to go. It gives you the most flexibility since it has raised sides and a lid, it can be used as a griddle or a skillet. We use those all in one skillet meals they sell at grocery stores. We also do pancakes and eggs. Stay away from bacon. It's smokey and you will smell it in the villas for days afterward (Even in a one bedroom). Don't do fish or anything that smells or would affect your
DVC neighbors. The best think about the skillet is it is very safe, and there is really no risk of fire.
It's funny that people say a studio is too small for more than two. The vast majority of families that go to WDW stay in rooms the same size or much smaller than a DVC studio.
We have stayed in a studio for a week with our two little girls and it works fine. A studio is much bigger and nicer than any RV you would stay in if you were camping, and it has a full bath as well. I say go for it, and let us know how it worked out.