I once went to a little country church where the only key the choir knew was the one that unlocked the front door. The closest analogy I can think of to describe their singing is a live peacock and a handful of ball bearings tossed into a Cuisinart at high speed.
But the Lord loved those dear, sweet, tone-deaf, sincere worshippers, and you could feel the Holy Spirit moving through that church every time that they sang. Maybe you should ask God to give all your worship team the desire to worship Him with all their hearts. It may not improve their singing, but if their "joyful noise" pleases Him, that's all that matters.
Excellence to God and excellence to man are seldom the same thing, I've found. But if the problem is really that bad, maybe you could offer some singing lessons to those in need of them.
Failing that, buy everyone a small personal microphone. . .and turn theirs off. :-)
Been there, done that, know how you feel.