I don't know of anybody who has moved a gray from one place to another every couple of months and, to be honest, I don't envision this bird doing well with this regardless of the cages or how hard you try to keep everything the same for him. Grays are the worst when it comes to changes... no parrot likes it but grays are on a completely different scale when it comes to stress. The other thing that comes to mind is that you will not have access to medical attention for him in case of an emergency, keeping him to a steady routine and schedule is going to be impossible and even providing fresh food daily will be a real challenge.
I use the Kings aluminum travel cage (http://www.kingscages.com/ProductDetail ... ID=ATT1214
) for my larger parrots and they are OK with it but they only use it for less than one hour at a time because it's only for the trip to the vet. I don't think that it will be good enough for trips between countries that will take hours and hours in it (too small, too confining). And I don't know of any good size cage for a gray that is easy to set up and take apart.
Personally, I would think about this VERY carefully because, most likely, you will end up with a plucking bird from the experience.