Have you ever scrubbed your list through a list cleaning vendor to confirm the validity of email addresses? That would be step 1. There are quite a few service offerings to verify email addresses and filter out spam trap addresses.
Did you conduct any sort of IP Warming/Domain Ramp-up campaign out of MailChimp? You said you've been sending to educators on a yearly basis - has this been from MailChimp, and have emails been sent from the same domain? It is a best practice to warm up your domain to let ISPs know you are a reputable sender, otherwise, you risk damaging your sender reputation and getting blocked/blacklisted from certain ISPs.
We work with a number of higher education clients that work in different ESPs, some of which are more advanced and have built-in deliverability tools and postmasters to help with monitoring. I am not familiar with MailChimp's deliverability offerings. The ESP you select depends on what your budget is and what services you are looking for, but regardless of what you select, you will want to ensure you are taking proper deliverability precautions.
At Fathom, we take pride in commitment to delivering excellent results to our clients. This means creating visually appealing emails that will render correctly across multiple devices, eliminating chances for a poor user experience.
To get buy-in, it's necessary to demonstrate the value and ROI of the tool cost you are requesting. Our team reviewed Litmus's capabilities - a built-in HTML editor, real-time rendering screenshots across multiple devices and clients, and behavioral analytics. Our analysis showed such an all-in-one service would greatly improve our team's QA efficiency, with other added benefits (an expert community, analytics, a real-time builder).
Our team demonstrated how such a tool would help our team and guarantee excellent delivery to our clients - making buy-in an easy approval decision.