Of course, this is not legal advice and if you plan to do anything related to this or any other legal matter, you should consult an attorney in your jurisdiction.
Please note, that although the following information is derived from the Digital Media Law Project and, thus, was created as a resource for journalists, the statutes it cites are generally applicable and so it appears the provisions would apply to you just the same as they would to a news reporter.
As you noted, Massachusetts is two-party consent. However, your answer is even more simple than that. In Massachusetts, "it is a crime to secretly record a conversation, whether the conversation is in-person or taking place by telephone or another medium." (Mass. Gen. Laws ch. 272, § 99). It applies to secret video recording when sound is captured.
Notably, a political activist who secretly shot footage of a protest after police ordered him to stop was convicted of violating this wiretapping statute (this was in a public place). However, the US COA for the 1st Circuit has held that the First Amendment independently protects recording police activity in public.
Additionally, the open meetings law in Massachusetts "expressly permits sound and video recording of public meetings (i.e., meetings of a governmental body required to be open to the public by law), except for executive sessions, by anyone in attendance.
Therefore, secret recordings are only potentially protected by the US COA for the 1st Circuit's decision, which may protect the secret recording of police activity in public. Secret recordings are not protected by the open meetings law (that law requires the would-be recorder to notify the chair of the public body and it requires that, at the beginning of the meeting, the chair "inform other attendees of any such recordings.") nor are secret recordings protected by the wiretapping law (again, which requires two-party consent).
I was wondering if it was legal to record public officials doing their
job as they are employees of the public school district, which in turn
is part of the state DoE?
If, by "doing their job," you mean attending and/or participating in, either as a guest or a member, of the public school board of the district you're talking about, then, yes, you may record them doing their job. If, by "doing their job," you mean what you allude to in your second submitted question, e.g., recording a private meeting in an office, then the "doing their job" part doesn't have anything to do with your answer, your answer will be based on whether or not all parties have consented to the recording of the conversation. Because your question mentions the fact that such people would rarely agree to being recorded, I'm guessing you're more interested in a 'secret recording situation.' In such a situation, no, it would likely not be legal.
Other assertions that balancing interests would prevail in favor of your secretly recording this conversation in order to get some sort of important information out there or something is specious at best. Practically, it flies in the face of applicable law. As user D M mentioned above, the quote from Glik v. Cunniffe goes far to distinguish a boundary between public spaces and private spaces. Conversely, the 11th Circuit in Smith v. City of Cumming, said, "The First Amendment protects the right to gather information about what public officials do on public property, and specifically, a right to record matters of public interest."). That, persuasive but not controlling in Massachusetts, would at least be closer to what you'd want to hear. Even there, though, it is unclear whether or not gathering info on what public officials do on public property would apply to a one-on-one meeting in an administrator's office.
If you can record police officers while they're doing their public
duty, you should be able to record public school officials during
private meetings inside their offices, right?
No. There is no connection, "if/then" or otherwise, tying together what you can do re: recording police officers vs. what you can do re: recording public school officials. The ability to do it for one has no bearing one whether or not you can do it for the other.