"My sole quibble would be the size of the tribe. 500 seems way too large; as I understand it, primate tribes have at most a few dozen members."

As rule of thumb the larger the group the more conflict within the group. Social mechanisms could reduce and/or lessen the violence of the conflict. Sports for example can be seen as a mechanism to REDUCE violence. Or said slightly differently, competition of any form can be a mechanism to reduce violence. Another example is role playing, as in men dressing up as females and mocking female behavior, is a mechanism used in some tribes, the value of which can be seen as means of reducing conflict. [this also turned around by the women role playing men, publicly mocking them]. For the people inside the system, this might described as a "fun thing to do", or they might describe it in other terms. There are lots of ways to reduce potential conflict and large portion of human behaviour can be viewed in this light of "reducing group conflict". The size of a group is dependent how how the group members "make a living" (economics) and larger groups can be more successful in warfare ("national security").
Small groups (couple dozen) will have less conflict* (require less mechanisms to reduce conflict) than a larger group (say 100 or more). I view 500 as merely a round number of the most number a group which interacts should be. Schools with 1000 students *could* be avoided. Obviously "a school" could have 1000 or more students if you organize it so a group of students interact with smaller groups- effectively making it a smaller school from the POV of the students and teachers.
But contray to this view, you could argue that a large function of schools is "social conditioning", therefore since in real life, students could be living in cities with populations over a million, large population schools [say 10,000 students] could seen as way of preparing students. Which I would see as somewhat valid, but you shouldn't organize a school which has smaller population [500 or less] in the same way you organize a school with 10,000 students.
Now, the above is "top down" type managing [which I hate]. I don't think there is any hard fast rules, rather I think of it as a factor "requiring attention". For example, I would view the govt mandating that schools be 500 population or less, as a bad and stupid idea. Though as a general idea to "work with" I think something which in kids were started in small groups and "evolved" into larger groups with these larger group having the "social organization" required MIGHT be an interesting "experiment"- which might lead to better citizens [more educated, intelligent, and socially rational].

*You actually didn't have humans only operating exclusively in small groups, interaction with larger population is required. This interaction was in form of marriages and trade. So small group of extented family unit, would consider themselves as part of much larger tribe, in which all the tribe may come together and meet every year or so, and/or smaller meetings take place more frequently and randomly. Of course warfare and "peace treaties" could be part of this interaction.