Havoc had what appeared to be a recurring URI that went on for like 6 months (off and on, with antibiotics). I was getting suspicous of the diagnosis because URI's are extrememly contagious, yet Toby never so much as sneezed a single time. I was on my 3rd vet when he determined my boy had plain old seasonal allergies. I gave him one last heavy round of antibiotics to knock any lingering infection caused by the mucus buildup, and then switched to over-the-counter allergy pills that are super-cheap and only used as needed. I also bought a table-top air filter thingy that helped a whole lot. I just used the air filter thingy for almost a year and the pills on rare occasions (maybe once a month) and didn't have a problem for almost a year. He started sneezing a bit a few weeks ago, but I give him a "booger" pill and he's good for a few days now.

I don't know how long you have until the J's go elsewhere but you might look into an air filter in with the room with the sickest one...just in case. The thing I bought was like 30 bucks and I don't know how I lived without it.