I've spent a fair amount of time the last several days educating myself about the options for finishing the space. Neither one of us has a background in any kind of trade that helps up do this kind of work. The closest I ever came to learning how to fix a house is watching my Dad teach my three brothers how to do stuff. (In fairness to my Dad, I wasn't interested in these kinds of projects at the time.) So, I'm approaching this project as one with barely a clue.
I had been thinking we might try to level the floor with a self-leveling mortar, but it turns out we would have to strip the paint off the floor first. That won't be happening this year. So, we're back with trying to find another solution. Sigh.
Yesterday, I found a suggestion for installing 2x4s, called sleepers, directly on the concrete, like joists, and then installing over the top of them. The Complete Guide to Finishing Basements, shows how you can install sleepers and then place shims under low spots. So, for now, that is our operating plan.
We're meeting with Tim Austin on Friday (he's the guy who built our garage) to see how much help from him we can afford. =)