If you're not building it specifically to compete in a profile event, you probably want to go full fuselage.
You can build a profile that's stiff enough and light, but you do it by building a hollow fuselage that takes almost as much work as building a full fuselage, and will never be quite as light or stiff.
I have a full sized Legacy kit that I'm building, and much of the weight of the thing comes from heavy wood in the kit. If you get a Legacy 40 rib kit and plans then you can select the wood yourself and mold the fuselage top to get more weight out, and you might just come up with a good solution.
Another option, which I suggest you pursue after you're comfortable building stunters, is a take-apart model. If your car will fit a 600 square inch model then it'll probably fit a 700 inch take apart. You may not need to do anything more than take off the wings, or even just one, depending on your car.