Darn... I wrote out a response and my browser closed randomly before it submitted
Here goes again:
Hi Ross and Erin,
I am inclined to agree with the comments so far.
In terms of cage size, it's too small for a grey. And as Lovemygreys pointed out, it's an awkward shape. For the same price there are some very good quality, larger cages. Since you're based in the U.S. they are readily available and generally have free shipping.
If you dog gets along well with the other birds, it will probably be fine with the grey. My CAG and dog tolerate each other. I think my dog is afraid of him. I'd just be sure to watch them when they're out together.
I'm biased, since I love my CAG so much, but I'd suggest a grey over a cockatoo. If your biggest concern about getting a grey is a propensity to feather-pluck a cockatoo may not be the best alternative. They are incredibly intelligent, beautiful, wonderful companion birds; however, if you are considering one it is important to know everything you can before you purchase. I have met several people who are in similar situations to what is described on this site who purchased a cockatoo and did not realize the amount which is required to maintain a good relationship with the bird:
http://www.mytoos.com
I've never re-homed an older grey, so I can't advise you on that. However, I did raise my grey from a baby and it was incredibly rewarding. How early you are able to take your grey home also depends heavily on the breeder. Some will not let them leave until they are fully-weaned. Others will let you take them home while they are still hand-feeding as long as you attend some sessions with the breeder. Unfortunately I only have a list of some local Canadian breeders, but I'm sure there is one online for those in the States.
I'd also suggest discussing this with an avian vet. They are usually acquainted with friendly, competant and reliable breeders and more than willing to suggest one.
Good Luck!