How can I force an iTunes Connect password reset?
Since you have shipping apps in the store, you will be able to call developer relations and begin the process to get things reset.

https://developer.apple.com/contact/ and https://developer.apple.com/contact/phone.php

Even consumer Apple ID have the ability to set a separate email address for emails about resetting the security questions and emailing administrative changes, so the account in question might very well be set up in that manner.

While you are on the line, you can ask about setting up multiple accounts for your business so that several people are listed to do certain tasks for you.