It would be interesting to know if the damage happens shortly after you leave, seeing he is anxious when you are leaving. Do you have a video camera or can you set up a web cam.
I have an intact boy in my house…there was a dog in heat in the neighborhood...the way I knew was because he was more mouthy than normal (nibbling on my arm, that sort of thing) and was slightly more anxious. He doesn't become more destructive during that time, but I'm sure dogs manifest things differently.
One thing I do is make sure the kids have things that are so thoroughly engrossing (kongs, busy buddies, etc.) when I leave that they don't notice me going out the door. Mine are all crated if I'm out all day...in which case, I hide treats throughout their crate (dehydrated liver, fish, that sort of thing), so they have to hunt for those...as well they get a kong and a busy buddy with their breakfast in it.
Also, I second the Patricia McConnell book "I'll Be Home Soon".