I really don't want to beat you about the head on this issue, but why would you trust the people on a public forum, most of whom can only speak from their own experiences? I've just taken a look at the requirements for a visit for marriage visa at Britain USA, and, as you've already admitted, you were in a hurry! Because it all seems to be there in black and white, the fact that he should write a letter, information about the wedding, etc.
So you ask if he should come to the US on a fiancee visa to get married? If he's just coming to get married and then going back to the UK, he doesn't need a visa, just his passport and proof of his ties to the UK, if he should be asked for them by an IO on entry. Others here may have more experience of that situation and can tell you more. A fiancee visa is for someone who intends to marry and settle (again, I'm guessing that it works pretty much the same with a US as a UK fiancee visa), not marry on a visit.
To me, it really looks like your easiest, safest option is to reapply for the MVV, including what you included before, but also, as Vicky mentioned, refuting everything in the refusal - include everything they said you didn't include last time.
If you decide to hold off on the wedding, and just want to come to visit, then your next safest bet, IMO, would be to apply for a visitor visa.
I have heard of others who married and lived apart for several years and visited back and forth with no special visas, just their passports, but if you have that black mark, I would expect (someone correct me if I'm wrong!!!) that you need at least a visit visa and a successful entry into (and exit from) the country to make it sort of disappear.
BTW, this is the link I looked at:
http://www.britainusa.com/visas/articles_show_nt1.asp?a=41191 I'm assuming it's a nice, up-to-date link, but I could, of course, be wrong! It's just the first link that came up for an American applying for a UK Marriage for Visit Visa.
Best of luck with whatever you decide to do.