I understand totally!! I am in the same boat with too many people with not enough time to keep going over parts!! It takes an hour rehersal to an hour and forty-five mins...
Simplify - the songs and the practice. Some praise leaders give out lyrics, chords, and recordings beforehand - that way there is no excuse for the "I don't know its". Can email music, words and links to performances on YouTube to the whole team.
As for practice, try having separate rehearsals (or parts of one rehearsal - have the instrumentalists come first, then give them a 20 min. break while you work w/vocalists. With your singers, have them practice with just keyboard, and focus on melody - that's the most important. Once they get that, put your strongest vocalists on parts, and direct the others to stand by and follow them.
And watch the clock! Have an attitude of "The sooner we get this done the sooner we can wrap up this rehearsal". Lots of time can be wasted over things like announcements, chatter and guitarists showing each other how to do chords, etc.
If they can't get the whole song right away, just do the chorus in worship...