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 passed.
This journal is by no means a top field journal, but it's a solid "good" journal. It's not terrible or predatory or anything like that. It's from the big 4 publishers.
Next, 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. This person's email address email@example.com is also the contact email under the "Contact Us" tab in Editorial Manager. One additional month passed.
I asked this question Is it acceptable to directly email the Editor-in-Chief if the editorial staff are not responding? on this forum. I then emailed the Editor in Chief at his institutional email, which was not listed on the website. That was about 10 days ago and he has not responded. All my emails have been polite, asking for an update on the status of the manuscript, etc.
This has never happened that the journal/editorial staff have simply not responded to communication, especially twice. What should be my next step? Aside from the initial confirmation email (after submitting the manuscript), I have never heard from the journal at all. (Aside: when I press reply to that initial confirmation email, it would go to the same firstname.lastname@example.org staff member as mentioned previously.) For example, I have received no email that a particular editor or associate editor was handling my manuscript. Thus, I can see the list of editors on the website, but don't know any of them personally, and don't know which of them is handling my manuscript.
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 try to contact the publisher directly. However, the publisher's website does state that for any request pertaining to a specific journal, consult the journal's website for whom to contact. So, what's my next step?