Have you tried a 'charity flight' appeal to the UK charter operators?
Monarch, Britannia, Air 2000, MyTravel all offer Atlantic travel (mostly to Florida and Las Vegas). If your case is genuine enough I am sure that one of them will be happy to publicise the fact that they gave your little girl a helping hand for free.
Air 2000 helps out a charity providing free hoidays for underpiviledged kids in Florida each year.
Try heading for the head of customer services at each airline.