My thoughts on this are mixed. For starters I have to seriously ask how there could possibly be that much stuff to spend money on in a game like this. The whole idea is blatently ridiculous to begin with.
What's more, I look at this from the perspective that their solution (if I read this right) is to have locked the kid out of the game and facebook, while still keeping the money? So basically they take over a thousand dollars and then prevent the kid from having the content that was paid for?
Personally if it was me, I'd be looking into the possibility of selling the items to other users to get some of the money back (some games apparently allow a trade in premium items). Either that or want the account to be active so I could try and sell it on Ebay or something (approved by the company or not).
Still, I tend to think the place to go is somewhere like the BBB or Attorney General's office. Technically you might not be able to force Zynga to refund the money legally, but you convince the BBB that the situation is inherantly insane, and they put the word out on Zynga... well that can cost them a fortune. If The Attorney General's office *really* wants to get involved (it can take some doing) that can work magic. Largely because nobody is totally clean and while they might not be able to do anything in court, nobody wants them looking at their business with a microscope waiting for the slightest slip up.
It's touchy, and not something I've really done, but I know people who have gotten results through both methods in various situations. Even if they deny you, if you write these guys letters every week, eventually you can get them to make a phone call, and generally speaking if either group actually calls a business and asks questions, simply the threat of them having their eyes on the company can result in a refund.
"My kid stole my credit card" is not that rare of a problem, and businesses don't like giving refunds in general for things like that especially if they take a loss, but it has ended happily in some cases... and incidently when you vote in state elections and such The Attorney General and his/her position on consumer protection and such is one of the things you should look at closely. Some are far more useful than others (ie some are pretty much owned by business, some actually run on a position of consumer protection and love to get good word of mouth from this stuff. Here in Connecticut our guy Blumenthal isn't bad for this by all reports).