You could open a ticket with 365 support and ask for some guidance. That's what I would do.
Note that "bulk" mail sending is not technically supported, so even though you may not be hitting established limits, the service is probably detecting the type or email and how its being sent as "Spammy" or potentially compromised.
That said, I have seen this many times and the choice is to either live with it, use a 3rd party solution ( recommended) or... open a ticket with 365 and let them know what you are seeing and how these messages are being sent, they may be able to assist. This happens to a lot of orgs and is not uncommon, nor is the request of many to somehow allow these type of mailings.