Thats 24% tax give or take. (thats 2% more than Footballers (Soccer) earning £100,000 a week pay here)
Serioius Question - Though you live in the USA, is there no way to claim the winnings as won in another country, i.e the UK, Gibraltar or Isle Of Man. Surely there must be some way of dodging paying $29,000 to the government for gambling and winning (as they see it). Couldnt you transfer some to someone, call it a stake or a gift or whatever. Then they send it back in the form of a cheque from their personal bank to yours?
Those ideas are probably the worst ones ever, but there must be some accountants over there who will "help you out" for a tiny fee compared to that?
Disclaimer - Is anyone official reads this, its not advice, its a general musing