Thank you all. I did a bit of research, and your responses combined with those from Slack leads me to believe we will not be able to use it.
A bit of info and clarification about what I was asking. I did some research, and when I asked about COPPA agreement, that, for us, is irrelevant since COPPA only affects students under the age of 13. Though some teams (even us in the past) have members this young, they cannot access most of the tech tools we use (other than Google Classroom due to COPPA).
It seems when our tech department says “They did not sign the COPPA agreement, therefore you cannot use their product” what they are really talking about is the SPDC. Because of RSA 189:66(HB1692) , the school is required to enforce that we only have apps that comply with the SPDC’s requests which are pretty much exactly what @zxsq suggests (and then some of course). Anyway, tldr, Slack did not sign it because as has been said, to sign it implies they would abide by FERPA rules, which they cant for people who are between the age of 13 and 16.
For me, the real piece even if legal did not get in the way is the inability to limit and monitor private messages. I feel that in it of itself is a non-starter. Thank you for your help. I will look into MatterMost, but I do not know about running a server right now on top of everything else.