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There is no built-in ability to do this. You also have to realize you're fighting a losing battle: if a recipient's mail server is intent on flagging your emails as spam even if you only sent to 17 addresses in an entire school district (which I'm assuming has at least 1000 email addressses, right?) then they will eventually punish you even if you send to those addresses over the course of a week.
Our experience in sending to institutions that have hardcore restrictions on sends from the same domain in <n> timeframe is that, frankly, no pace is slow enough -- we would never be able to send them a second email on time because we'd still be spacing out the first email over weeks and weeks.
That said, you could play with segmenting the list -- and send times -- by letters of the alphabet or something like that. It's not a truly random distribution, of course, but maybe the spacing would help. I wouldn't be hopeful. Also realize that they may be considering your emails, content-wise, as spam (that phenomenon of "false opens" means that their server is parsing the content, downloading images, etc. before considering delivery to an Inbox).