Chad,
You say it is "smooth as glass" and that it "cooks like a dream" so I must assume you have been using it. If you like the way it cooks, why do anything at all? I understand Cheryl's perspective of not knowing where a skillet has been and the desire to clean and season a piece of cast iron. You could use the oven cleaner and plastic bag method. But in this case, I think you should consider just using it. I see no reason why you can't clean it later when you have the space.
If you want to try oven cleaner, here is what you do. Using good rubber gloves, spray the skillet with a lot of oven cleaner, inside and out. Then seal it is a plastic garbage bag. It helps to put the bag in the sun because the chemical reaction that strips off the residue works faster if the pan is warm. The point of the bag is to keep the water in the oven cleaner from evaporating. After a day or so, pull out the skillet (remember the gloves) and scrub the loosened residue off of the skillet under running water. Use a stainless steel scrubber like a Chore Boy. You may have to repeat the oven cleaner and scrubbing procedure a few times to get all of the residue off the skillet. Once that is done, you can assess if the skillet is rusty. If there is just a slight amount surface of rust, you can season the skillet right over the rust. It will not interfere with the seasoning process. There are a lot of seasoning methods on this forum that you can follow.
Good luck.