OK, I finally have some time to get back to this. Thanks for all criticisms () and suggestions.
As time is not in my favor, I did contact a small-repair concrete guy in town to get a quote, but he was too busy to connect with me when I was available. I figured that I can and will do it on my own anyway. As I mentioned, I took out a book about masonry from the library, which also has a DVD. After reading/viewing, I am confident that I can do it.
Filling stone is the easiest option, and also my least favorite. Too much traffic and potential erosion.
I like the like the idea about cutting across and making the space trapezoidal. The sides will not be parallel with the mismatching dimensions of the side and it will have a somewhat odd shape, but unique is better than boring to me and I think it'll look very cool. It will up the price a little though, as renting a saw w/ blade for the job will be up around $50 (not including the extra concrete necessary for a larger void). I don't want to use my circular saw because that could throw off it's calibration with such rough cutting. I am going to check out some chisels. Somehow, I will make that cut, I'm just not sure how much I want to spend on that aspect.
I also really like the idea of creating an aggregate surface. That will be a plus for traction and appearance. This is also covered in the book I have and I think it'll be totally doable. And it does look fun.
Oh, and doing the sections one at a time seems like the way to go, especially after seeing how screeding is performed.
I will be back with my progress at some point.