Can you reference a CNAME record in an MX record?

According to RFC 1123, the MX record cannot point to a CNAME. If I were in your situation, I would setup mail.ourdomain.com as an A record pointing to the new suppliers IP address and then quickly work on changing all MX records over to the correct data. Then address why changing MX records is so difficult in your organization.

That being said, most mail servers will still submit mail to a CNAME; however, you can't be guaranteed of it.

There are companies that provide Backup SMTP Service aka email store and forward. Perhaps you could use one of those companies to wash the IP for you.

If they can't be the permanent middleman maybe just having them as a secondary MX record will help with the transition process so you don't have undeliverables bouncing around.

If you are currently speaking of one of those sorts of companies maybe you could second source it and have them forward back to the first source.