Great. Thanks for the additional information. I really appreciate it.
It sounds to me like Otis may be dealing with a little anxiety based on his history of being given up when he was a puppy. It sounds very much to me like he is very bonded to you, and when you go away, it confuses him. When you get back he's working through that anxiety.
There are a couple over-the-counter products that you could try that reduce anxiety in dogs:
Melantonin is an over-the-counter drug that can be used to treat some anxiety issues in dogs. The dose you would give would be up to 3 mg given orally whenever necessary up to every 8 hours. More information can be found here: http://www.petplace.com/drug-library/melatonin-melatonex/page1.aspx , which includes risks, warning signs to watch out for and other bits of useful information.
Try a DAP collar. These are collars that are impregnated with a man-made version of the dog appeasing pheromone, which is a pheromone that nursing bitches give off to their pups to help them feel calm and secure. It's something that humans can't smell, but it has an amazing effect on dogs with anxiety and other issues. Although you can find them at your vet's office..you can also find them online at places like Amazon.com and Ebay for much cheaper. Just make sure they're DAP brand, as they seem to work better than some other versions.
If this were me, I'd actually use the collar. It's good for 30 days, so you can put it on him when you leave town, and he wears it while you're gone and when you get back. It should help take the edge off.
I hope this helps.