John, to make your dish an oval or any other shape for that matter, just cut off what you don't want! You just have to make sure you have enough aperture area left over that it will be equal to the 10' dish surface area. The bottom line is that if you are set on a dish you want the energy focused on a point, to focus on a point you need a dish. So calc. the area of a 10' circle and compare to a 12' circle with 2' cut off the top and bottom.
Now who has the Stirling Engine. If I had an engine, I would have built a dish. And like you I wanted to keep the profile low, so I thought about the modified dish, but sunlight is energy and I'm collecting. I'm using a trough, real low profile.
But if I had a Stirling.............