I haven't read the whole thread, so forgive me if I'm redundant. I did read the first few, and Jonathan, I totally agree with you on the kids in ministry piece.
Anyway, O1A78, my personal belief is that rehearsal isn't the place for teaching and prayer service and Bible Study and all that extra stuff. Personally, I hate rehearsals like that, but that COULD BE because I have a very short attention span. I strongly believe that teaching should be done at Bible Study, or if the director (or membership majority) feels strongly that there should be study, you should add it at the first half hour and not make it a part of rehearsal. But of course, that's just my opinion.
Since you take this whole thing so seriously (which is great), I would suggest that after the prayer, you go into a worship/warm-up song. And instead of monitoring them, go into worship for yourself. Close your eyes, and get lost in worship. It may take a while, but I really believe that after a while, the right song will hit them on the right day at the right time, and they'll start to feel something. If nothing else, they'll come to see that time as worship time, not play time. People will begin to catch on after a while. And you'll be a lot less frustrated if you're not watching them waiting for them to join in.
Another alternative is to determine that the choir is for worshippers and praisers only, and if they can't demonstrate that worship and praise to God while singing for His glory, then the choir isn't for them... kinda like what Jonathan said: cut the dead weight. So what if they can sing? I'd rather have true worshippers than a bunch of melodic parrots, personally.