In answer to your question "What leverage does an author have ... ?" , I would say, "Fortunately, none!".
That probably sounds harsh but if it were the case that you had "leverage" then so to would everybody else, suggesting that it would be leverage, rather than merit, that resulted in papers being published.
It is the job of an editor to cull through hundreds and hundreds of submissions and to select from among those submitted, the few that best fit the goals of the journal. It is the job of a reviewer (and I used the words "job" very very loosely since most reviewers are unpaid) to assist the editorial team to do their job. Because the number of papers submitted to a journal usually far exceeds the number that can be published (or even read completely), the first task of a reviewer is actually the exact opposite of what you might think. It is to read enough of each paper to be able to decide whether it is unpublishable. Since the vast majority of papers reveal themselves to be unpublishable fairly quickly, a reviewer can devote more time to the few papers that are (double negative here) not unpublishable.
It is your job and yours alone to ensure that the alarm bell for unpublishable is never sounded in the mind of a reviewer. Again, my comments might sound harsh but a brief digression will illustrate my points so far.
A colleague of mine is a major review-handler for a funding agency. Because a funding agency gives money away for nothing, the number of submissions is high and funding-reviewers face a worse nightmare, with even tighter deadlines, than journal reviewers. My colleague conducted a double-blind experiment over a few years. To one group of reviewers, she sent only the first 150 word abstract of each funding application and asked for an "accept/reject" decision. To the second group of reviewers, she sent the entire grant applications, again with requests for "accept/reject" decisions. There were no funding applications that got a rejection based on the 150 word abstract yet received a positive rating on the full application. In other words, out of a 5000 word application, most could be rejected on the basis of the first 150 words.
I know from harsh experience how annoying, frustrating, and downright discouraging it can be to receive so few comments, or such contradictory comments from reviewers, that you cannot see how to overcome the apparent impediments to publication. But while I understand how nice, helpful, useful and encouraging it would be to receive detailed information on improving your publication, you have to understand that no one owes you. The system is not broken. It is not an obligation of the reviewers or of the editors to try to understand or improve your paper, nor even to help you to improve it. It is your responsibility to make it so clear why your paper is worth publishing that an editor will be doing everything they can to get your paper into print.
Extended response to your comment
I hesitated over responding to your comment because I don't wish to offend you. I do understand how extremely frustrated you are with feedback that has not so far enabled you to get your paper published. However, there are things in your original post and your question that shed light on at least some problems.
First, and as a somewhat minor issue, I assume that you are writing for an English language journal and that you are not a native English speaker.
Second, and far more important than the native-quality of your English, is that your ideas are not, in my view, expressed clearly. Consider, for example, two sentences (one in your original post, one in your comment) that relate to the same issue.
- Original post sentence: Review reports from our previous journal submission did say that this is a well written article that puts forward important ideas. But they criticized the overall article's structure and some of the used references.
- Comment sentence: This paper was accepted by 3 journals. Two of them were pretty high ranking.
When I read your comment I initially thought that I must have completely misread your original posting. I thought "Wow, this person has already had their paper accepted by three journals and they're still unhappy!" But I had not misread your post. Instead, you have not consistently expressed yourself clearly. That might be connected with your successive rejections! If I have pieced together the information correctly, what you really mean is something like the following:
We have now submitted our paper to three journals, two of which are fairly high ranking, and we have had the paper rejected by all three journals. In each case, the paper has gotten through the editor's "desk check", without being rejected, and has then been sent out for peer review. After having been peer reviewed (now three times!) we have received rejections from the journal editors, accompanied by mixed reviews.
From this, you have some useful information. The opening of your paper expresses itself sufficiently clearly to make three editors think that it will not be a complete waste of time to ask other people to read the remainder of your paper carefully. What then has gone wrong? From what you have written, I don't know! Instead, I have made some guesses, and made suggestions. The guesses are not in any particular order.
- As I argued above, the evidence is that you do not consistently express yourself clearly. Solution: have an experienced author (not necessarily an engineer) read your paper and give you feedback about your writing.
- Your paper might simply be a poor fit for a particular journal, in which case, continue your search. I think, from some of your remarks, however, that this is not the problem.
- You oversold your ideas in the first 150 words of the paper and it appeared to be more interesting initially than it later turned out. The editor was impressed by the initial sell, but the reviewers saw "hot-air" rather than real substance.
- You can express yourself very clearly in your native language and might also be a very good speaker of English but you are not so good at expressing complicated ideas in English. Solution: if necessary, pay a native English editor to help you improve your paper.
There are numerous other possibilities. I suggest that you also read this question (which reflects struggles that are similar to your own) ... and this answer.