I'm glad you love the project. I had a lot of fun working on it. When I remade the piece for the article, I considered using an oval stone, too, but I decided not to, to keep the instructions simple. I think you could use the same instructions for an oval stone, you'll just have to add or decrease the number of rows to fit around the stone, just as you would adjust for a different size round stone (see the note on p. 47).
The only problem I can see you running into is that the bezel might gather differently on the narrow edges of the oval, versus the longer edges. Whether or not this makes a difference would depend on the shape of your oval. You might have a problem if your oval is long and narrow, but if it's fairly round, you may just be able to follow the pattern. One way you could adjust the bezel to better fit an oval would be to use both 15/0s and 11/0s in the center ring on each side (step 10 of "Pendant"). You could use 15/0s on the narrow edges and 11/0s on the long edges. If your oval is long and narrow, you may need to skip adding a bead at some points as you tighten the bezel. You'll have to experiment to fit your particular stone.
I hope this helps. I'd really like to hear what solutions you find to using an oval for this project. Happy beading!