I was in the same situation in reverse, Drew. I ended up getting married and staying here. I probably can't give you any decent advice but there are ways around the official system that are worth taking.
There were various loopholes to squeeze through - for example, if we'd have declared that we intended to get married, they'd have said "oh, that's nice - if you'd just pop back to Britain now and we'll let you know when the paperwork is ready, shouldn't be more than six or eight months". I had no intention of going back to Britain and sitting there, so we got the wedding arranged, I arrived back in the US on a three month visa, we waited two months (to make it look more realistic), we got married and presented ourselves at the equivalent of County Hall. They had no problems letting me stay doing it that way.
Later this month I can apply for US citizenship, which I will take if I can get dual citizenship (I will not give up my UK citizenship). To get US citizenship you have to "denounce" any other country you've ever pledged allegiance to - the loophole being that I've never pledged allegiance to the UK so don't have to denounce it, thus keeping both citizenships.