What about getting married in the UK instead?
It's a longer process to marry but if he can't travel it might be the better option.
You could either get a Marriage Visitor Visa to marry in the UK as a visitor, but you would need to return to the US after the wedding to apply for a spousal visa. It costs about £87 and is valid for 6 months, however, you would need to be able to spend at least 35 days in the UK (possibly up to 77 days) before you could marry.
Or you could apply for a 6-month fiancé visa to move to the UK, marry and then switch to an FLR(M) visa (in-country version of a spousal visa). The fiancé visa has the same requirements as the spousal visa except you show you are planning to marry in the UK instead of already being married. However you cannot work or study until you have the FLR(M) visa and you will not have NHS access on the fiancé visa either. The fiancé visa is valid 6 months and costs £1,195, then the FLR(M) visa is £1,311.
Or another alternative might be to marry in a different country, if he can travel there, and then you return to the US to apply for a spousal visa.
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