Yes, I've known quite a few people that have oxygen at home for their dogs. Most people make a coke-bottle mask (lay the mask near the dog's nose while the dog is lying down) rather than making an actual cage. You can make a cage with a crate covered in plastic, but you must be careful because the carbon dioxide (from exhalation) needs to be able to escape the cage. I can print out instructions on this and scan and email to you. You can rent oxygen tanks, etc., but I'd probably buy them if I had a dog like Kennedy. Actually, I'd probably buy or rent an oxygen concentrator rather than tanks that had to be refilled. You can sometimes buy one on ebay.
I still think that none of this is cardiac related, it is all airway disease.
I also think that weight loss would be very helpful. 30 pounds seems very heavy unless he is a really large framed dog.
What does your friend think about the diagnosis of eosinophilic stomatitis? I presume that no one had a clue about this before? I think the GP vet (who may be a nice person, etc.) is totally clueless, FWIW. The standard treatment for stomatitis is prednisone since this is an immune-mediated disease. Pred can also help inflammation and airway disease. But the side effects are going to be very difficult for a dog that is used to eating a lot and who is already overweight. This is a very tough situation.
Air purifier isn't going to do much, and you don't need a humidifier as long as there is central air-conditioning. Keeping the house very cool during the hot, humid summer will be essential.
I'll try to send you info on oxygen tomorrow.
Pat