Congrats on your new pets. You have certainly come to the right place for information.
There's all kinds of utterly terrible bits of information on the Internet regarding chinchillas and diet.
I can see there's a few things you've got going on that I think you'll want to address.
I'm not too concerned about George but the new chinchilla may need to see veterinarian to have a dental workup and check for liver enlargement/ lipidosis. If both are detected you'll be better off keeping the chins separate because of potential disease.
Chinchillas should be on a diet of plain alfalfa-based pellets plus loose timothy hay. The hay is actually the main diet and the pellets are considered to be supplemental. There are only about 4 or 5 brands that are really proper for them. The best ones are easy to obtain in the US. I'm going to recommend Oxbow Chinchilla Deluxe or Mazuri chinchilla diet. These are time tested feeds that have known to produce very long lived animals. There are others but they come with caveats. TSC will provide Mazuri but you have to special order it. It's a pain but the cost savings are significant for a 25lb bag. And you know you're getting a top quality diet.
Feeds that are a mixture are usually horrible, as in toxic. A chinchilla should live at least 10 years, and with these novelty diets you can't expect much more than 2 or 3. Usually death is from dental malocclusion when it's diagnosed but I think organ failure is a contributor. Chinchillas are prone to lipidosis from oily or fatty diets which have seeds and nuts in them. Sugar is known to cause cavities and you can imagine they'll pick out the sweet garbage, don't get normal wear on teeth, and end up malnourished as well.
Dental problems seem to be the worst for chinchillas. Once they start recovery is very rare, very expensive, requires multiple treatments, and just usually evolves into a sob story and a dead pet. Considering the history behind your new pet I advise getting a dental x-ray and full exam there to make sure you're not dealing with something like that. Lethargy is usually the sign of something very serious but there could be other factors such as its normal routine, as most chinchillas sleep during the day and are most active at night. They can adapt to their owner's schedules though.
As far as relocation stress that is usually a problem that's easily solved. Just avoid a lot of handling for the first two weeks. With any chinchilla that is not well socialized start slow and build up. Read your pet and try to make sure its happy experiences with you outweigh any stress associated with handling.
As far as Timothy hay I really don't think it matters but I know others have arguments to be picky. I'd be surprised if there are additives. If there are it will be listed and I've yet to see that in packaged loose hay. Of course I stay with brands I know such as Oxbow and Standlee.
One thing I have noticed is that moisture can be a problem with hay packaged in plastic and I've learned to open the bag and smell it before I buy it. But lately I've gone to buying large bales and storing the hay in mesh bags because it's so much less expensive. As long as it's green and smells good it's fine.
I'd say find something quickly, doesn't have to be same day or anything, but I think you should change diets soon. I think it might be wise to get a vet exam and keep your pets in separate rooms in case it's something contagious like a respiratory problem. Animals should be kept separate anyway for 3-4 weeks for observation. Because relocation causes stress, an already compromised animal could be in really bad shape. Please be aware of that and make sure you know what's going on.
I'd be glad to ask any questions you have.
