Keep in mind that this is a forum for Americans who want to live in the UK, most of us don't have a lot of knowledge about how the process works in reverse. However, I have heard that the US fiance visa is hugely expensive and takes ages--6 months or more. Plus, it's for people who want to settle in the US, so I don't think you'd be granted one.
ETA: I've just googled "B2 visa extension" and apparently it is possible to extend them, for up to a year. You might do a similar search of your own for more details.