Tim wants to try to leave him in the livingroom and kitchen to see what he does...I'm not so sure!
I agree with you! Don't overwhelm him by giving him too much freedom at once. Try the kitchen until you are absolutely sure he will be fine loose and then you can expand his area.
He sounds like a wonderful dog and I'm sure once he feels secure, his problem will fade away.
Also, the most important thing for shelter, rescued and abandoned dogs is routine! Knowing what to expect next is the most vital thing of all. So try and give him meals, playtime, walks, etc at the same time every day for awhile.
This will build his confidence.