I have submitted a paper to a journal that says the time to first decision is generally X months, and that there are strict deadlines for reviewers to complete their review. After X months were up, I used the journal's internal submission system (Editorial Manager) to send a direct message to the editorial office, with no response. Two weeks after that, I searched the journal website and found an email address of a staff member to contact about the submissions and peer review process. This staff member appears to be a full-time employee of the publisher, rather than an academic. I emailed the staff member, and also got no response. It has now been another month since I emailed the staff member.
Both of my emails were very polite, asking for an update on the peer review process, and this has never happened that the journal staff have simply not responded to communication, especially twice. What should be my next step? I can contact other staff members listed on the journal website (who deal with different matters such as author proofs after the paper is accepted) or I can contact the Editor-in-Chief directly. His email is not listed on the journal website, but I can easily locate his institutional email. What should I do - is it reasonable to email that?