If you want the most value- sell it yourself.
If you want a better car (one that you may qualify for now)- trade it in while your car is still worth something. (200,000 miles is a lot)
If you want to run it into the ground- be prepared to start from scratch.
You said that you want to switch from full coverage to liability. This is by far the dumbest thing you can do.
If you get into an accident, at least you will get reimbursed for the value of the car (granted that it's totaled). Well, even if it's not totaled, you would only have to pay the deductible if you needed work on it, which usually isn't cheap. If you have liability- YOU WILL GET NOTHING.
In my lifetime- I let my insurance lapse on 2 separate occasions- for a week's time, both times.
Sure as shit, both times I got into an accident.
The first time it was my fault, the second time it was someone else's.
That doesn't really apply to you- but I guess this is my point-
You pay out the ass for something (full coverage) and you think it's a waste because you don't get in an accident, so you decide, shit, well I may as well just get liability. And that's when something happens. Murphey's Law is notorious for shit like this.
Just shell out the extra couple bucks (for full insurance) because it's worth it.