Do all your school naming conventions have the same number of characters as the designation? For example, in the example above, you state that a school uses "31203" as the code, and therefore the assigned computer name starts with that. Do they all follow that model that the first 5 characters designate the school name the Mac belongs to?
If the answer to the above is yes, then I would suggest setting up an Extension Attribute that will grab the first 5 characters of the assigned Mac name and place that into the result. Once that's set up, you'll then be able to use an exact match, or "is" instead of using "like" which can end up sometimes grabbing systems you don't want to grab into the Smart Group.
You didn't mention if the issue is that the Smart Group is getting too many Macs or not enough Macs. If it's the former, then the above may help. If it's the latter, I doubt it will make any difference, in which case you may need to figure out why it's not matching up.
One thing to keep in mind is that Smart Groups can only get managed machines/devices in them, so if the discrepancy is only off by a little, is it possible you have a few machines that aren't managed in your JSS?
Also, I thought we were able to use Prestage enrollment as criteria to search on or build SGs on? Is that not the case? If it isn't, then that needs to be a thing.
