I've never actually used the request menu! I'm usually at BWV and there must be something in my profile that says 'will take the crummy view down by the tennis courts' lol. That's where I like to be and mostly because of parking and bus stop.
I do try to get to the desk early - I never do online check in because that requires a credit card and they don't get my credit card. I think Florida is the scammiest place for using CC's.
The rooms are already assigned by then, 'but' they are constantly reassigning to accommodate people who arrive earlier etc (those that complain and raise a stink) and there is always a chance they will try to give you what you want.
Of course nothing is guaranteed. The new day opens at 7am, so if you are in the area, say at a WDW resort or offsite, it may be worth a shot. I've actually gotten into a room at 7am. Mostly when I was staying at BW area resorts with split stays. Now it's a little more difficult as occupancy is much higher and they have this thing where if they sign you in it checks you out of your other WDW room, which isn't a problem if someone is still in the room(you own the room until 11am), but it makes your keys not work.