I'd go with 5 judges, drop the high and low to make it more fair. hey use this in some sports to keep things more fair.
I'm assuming the payout is for anyone in the semi-finals in the winners bracket and the one person from the losers bracket.
If you're going to do a contest over a period of time this solves a lot of the normal issues associated with them. You still have to deal with the areas they rate them in and other issues but its a start.
I'd probably have them only sing each song once though. Just to make it more interesting.