Honestly, I am going to bet he looses in the end. The US government has unlimited time and will around these things (look at what they did to the mob). Let’s say he steps one foot out of the UK to another country that has an extradition treaty, US issues warrant and it starts all over again. It is likely given the fact that the UK judges only reason for not granting the request was how he would be held that the US government as we speak are drawling up a proposal that would be agreeable to the judge.