I'm dealing with the same thing with my tee-ball team, which is 5 and 6 in our league. I've gotten to the point where I've essentially stopped working on catching and some of the basic fundamentals (and moved on to hitting, baserunning, and what to do when fielding a ball in the infield or outfield), because one hour once or twice a week with twelve kids just isn't enough time. I'm in a similar situation where I have three very solid fielders and then 8 others who are new to the game. That said, I'm fortunate that they are all good kids and listen well for kids that age.
Speaking for my kid, his catching has come a long way in the last year, and especially the last couple months, but it's really just been about reps. I bet I've thrown a thousand balls to him in the last month. We usually start out close together and I tell him where the ball is going (low, backhand, forehand, overhead), just to get his glove loose and to get his confidence up. We used to do a lot of barehand but have gotten past that now. Then we just play catch. I wondered for a while if he was ever going to pick it up, but has really clicked as of late, just based on reps. We used the SWAX balls a lot and have only moved over to real baseball full time in the last few weeks.
If those kids are going to learn to catch, it's going to have to be at home, IMO.