Why can't governments come to agreement on this?
If the US laws were broken, allow the US law and sentencing to apply but he gets jailed in the UK. Likewise if a US citizen hacks the UK, UK law and sentencing would apply but he gets jailed in the US.
Then there are no concerns about how he's treated in prison or distance from family. If the UK government is concerned about length of sentence, maybe they can help represent him in the trial or plea bargaining negotiations.