Well, I've got a temporary verdict - finally got Jake back into the vet, and it looks like he's got an upper respiratory infection - most likely caught off of our new addition, our rescue kitten Alley. It's weird, because Jake's shots are pretty much up to date, but so be it.. He'll be on antibiotics for the next couple of weeks (he'll love that - he was just about done his other medicine too - poor guy), but the good news is hopefully he'll be all cleared up after this. We'll get him a booster after that, and maybe this will be the end of it..
Then we're on to weight loss - I picked up some cans of Wellness, so we'll see if he can drop down to a managable weight soon enough - the light food definitely didn't do him any good!