I don't know how you feel about this, but I would put Jasper's crate in another room and emcourage Piddle to come sleep with you again. Even that little change could contribute to helping his depression.

A new dog is very stressful and a lot to handle for the resident dog, especially if the new dog is a young puppy. You might want to also consider baby gating Jasper into a small part of the house and letting Piddle have free roam of the rest of the house for a couple weeks. Also, socializing Jasper with other dogs will help burn his energy so he won't be as interested in messing with Piddle (not sure if he does or not, but most puppies can't resist tormenting other dogs).

I would talk to your vet and try to figure out a way to get Piddle back on dog food. Well I wouldn't do that until after you get him over his depression though. Trying to fix too many things at once won't work well.