I think SoR already has announced that it will go on tour as well, or am I mistaken? If so, I'm sure it will come to LA as well.
I don't think the SR original cast will stay much longer. I'm blanking right now, but I already read something Christian Borle is gonna be doing, and Brian Darcy James might go do more TV work (or go back to Hamilton?). So if you wanna see them, see it now. Personally also liked SR way more than SoR. I found the music catchier, and it's just SO much fun. SoR was cute and the kids are very talented, but that was about it for me.
Aside from those two you were already thinking about I would recommend Daddy Long Legs Off-Broadway. Not sure if you would consider a very small, intimate show (2 actors, 3 musicians, 1 set) that is much more quiet that then 2 you were considering. But it's a beautiful piece of theater and by top recommendation for everyone right now.