A nice review, Kate! Very well-written. Larson is a good choice relating to this topic (though I clicked out to have a read and it ate my first attempt at a reply! :P).
In the work I’ve done with public libraries in the past, kids’ activities almost always go over the best. Most of the activities are held during the school holidays, with a few more frequent ones in the time between when school finishes and parents get off work. It’s great for the kids, who always enjoy it, but also for the parents, who are often just relieved they’re not the one singing Baa Baa Black Sheep or reading Don’t Let The Pigeon Drive The Bus (protip: check this book out, it’s amazing and kids love it) or combing cornflour slime out of their hair for the fiftieth time that day! I’m of the firm opinion that this kind of group play/”learn by playing” is the best way for kids to learn in the early childhood years. As Larson mentions, having a certain structure and certain “rituals” can really help as well – most kids get a lot out of having a set routine, doubly so for any special-needs kids you might have. It can be as rigid as “We read a picture book at 4:30” or as flexible as “When we get out the floor mats it’s time to sit down and read a book”.
One thing that I didn’t see mentioned was including older kids (10+) in children’s activities as “helpers” or co-presenters. I’ve found this is a great way to get more of the community involved, and having that little bit of responsibility is really good for kids around the middle school age.