Seek the menschen and ye shall find.
Have a look at the NCSL, but understand that while games are most often scheduled for Sundays, there are often Saturday games, too (though not necessarily morning games, so if you drive on Shabbes it could work.)
If that seems ok to you, take a close look at team culture and coaching. They really run the gamut. There will be coaches who have no interest in taking on a player who will likely not be available for key tournament games -- and there are coaches out there who are more interested in the humans they coach than in W's and L's., and will gladly consider your child if they would otherwise be a good fit for the team (and if the team would be a good fit for them.)
You'll know the menschen when you find them.