Soontobeharrison,
I wish you luck with your fiance visa at the LA office, I would hope you will have a answer soon, depends on who you get there it seems, some have had no problems while i had every problem and hurdle thrown at me at the la office.
If you have everything in order i would assume it wont take to long, (mine was 7 months start to finish)
If you have any trouble ask for the deputy consulate (wish i knew that long before), seems there's 2 they are both nice and helpfull, avoid i repeat avoid Paul stevens (hes the boss it seems who doesnt care what happens).
Some advice here also, have with your application
Plane tickets for your departure to uk (proves your intent to move to uk)
a wedding date (if possible) or a intended date for wedding if you cant get a exact date (church wedding or town hall etc..)
pictures of you both together (proves you've met)
any emails or letters writin (didnt seem to bothered with mine tho)
Be prepared for them to request you come to La for a Interview( they stated it states you "may" on site)
I was givin 2 and only 2 dates or my application would be rejected ( the following day and a day the next week)
I was very lucky i got help from the deputy consulate (both are very nice and seemed concerned i had such trouble)
Wish you luck make sure you have everything in order and all should work out.