How do I publish papers taking a middle ground on a controversial topic, when reviewers with strong opinions on either side keep rejecting them? In the last few years I have been working on a controversial topic A of my field. As usual, I started doing the state-of-the-art and talked with some scientists, and I discovered that the scientific community is divided in two groups:

~80% of the scientists don't think A can work
The remaining ~20% think A can work

It's difficult to formally prove A (no one has done it yet) and basically not possible to experimentally verify it (we only have some not-so-strong empirical evidences). There are also some sort of philosophical issues (even if the topic is really technical). However, if formally proved, it would have a huge impact on both research and industry.
I think that group 1 is wrong and also group 2 is wrong. The truth, in my vision, is in the middle, and my research focuses on this: trying to find a different modeling or trying to formally prove only part of A, or A but with some extra assumptions, and so on.
However, during the years, these two &quot;factions&quot; started to diverge more and more on opinions, to such an extent that the group 2 now always bases their claims on a couple of very controversial papers (which most people, including me, think are flawed). This way of reasoning of group 2 made most of the community (group 1) to believe that any research claiming A is just wrong (which is not true).
And then, there is me. Probably because I arrived at a later stage of this &quot;discussion&quot;, I see things in a different manner: there is hope for A, but we need to recognize the limits of A and the fact that the state-of-the-art works on A have problems. However, when I submit a paper on this topic (from a position paper, to a super-technical paper), I very often get reviews like:

From group 1: &quot;A is a shitty thing&quot;, &quot;Oh no, another paper on A&quot;, &quot;This is not interesting for the community&quot; *
From group 2: &quot;We already proved A, why we need this work?&quot;

*These are textual transcripts of sentences in reviews of top conferences/journals.
And often these reviews are opinion-based and not fact-based, which make me very frustrated, because they don't criticize the work itself (formal proofs, etc.), but the topic.
Luckily, I have sometimes received reviews that really appreciate my work and some scientists have told me that my way is the right thing to do. However, publishing (especially in top journals and conferences) is very difficult in this way, because I always get at least some reviewers against me (in one sense or in the other, often both of them). Editors most of the time don't care about the controversial reviews, they just reject the paper.
What I'm doing now, for papers on A, is to publish in less-important journals or in journals not 100% on topic, but this reduces the visibility of my works (and unfortunately impact my career...). This makes me sad and I'm really thinking to abandon this topic. Getting a rejection is always frustrating, but getting many rejections based on opinions is really terrible...
I don't know if there is a solution or what I should do. For the pure research spirit, I may publish just on Arxiv or so, hoping that someone will notice them... but you know, an academic career requires you to publish, and to publish in good journals/conferences...
Any suggestions?
A principle in rhetorics and the art of persuasion states that it is useful to preemptively address any criticism that you expect will be leveled at you after you make your argument, by raising the objection yourself and then explaining why it’s not valid while you are making the argument in the first place. * If you do this in a thoughtful way, a potential critic might be converted into a supporter.
Thus, instead of laying out your case following the rough template of

[make a claim/hypothesis/etc]
[present first supporting argument]
[present second supporting argument]
[etc]

you could instead use a structure such as

[make a claim/hypothesis/etc]
[present first supporting argument]
[present second supporting argument]
[etc]
[raise first possible objection, then address it]
[raise second possible objection, then address it]
[etc]

Now, it is not always possible to foresee all objections that could be raised by someone. (This is especially true since we are mainly thinking here about objections that are invalid, and can therefore be successfully defended against!) However, in your case you have already heard the main invalid objections raised several times, and can therefore preemptively defend against them according to this recipe.
Here’s how this can work in practice. The way to defend against the objection

&quot;Oh no, another paper on A&quot;

Is by making it very very clear in the first place that your paper is not “another paper on A”. That is, suppose that in the introduction to a rejected paper you wrote

In this paper we show that A can work in a scenario in which [some extra assumptions].
[proceeding to describe your solution]

While accurate, this may not provide enough context to differentiate what you’re doing from the typical “paper on A”, which can lead to the sort of knee-jerk reaction from the reviewer that you quoted. Instead, maybe write something like

Many papers have been written claiming to show that A can work. We do not make such a claim, and indeed believe the earlier attempts to show this are incomplete and that the problem may continue to resist attempts at a rigorous solution because of the inherent difficulty of either formally proving or experimentally verifying A.
Instead, our goal is more modest, and therefore more achievable. We show that, if one is willing to assume [extra assumptions], the problem becomes tractable. In that case, a version of A can indeed be made to work through a reasonably straightforward application of [technique].

It seems to me that someone from the anti-A faction is likely to treat your claims with a bit more respect after a paragraph like this.
Similarly, the second objection

We already proved A, why we need this work?

can also be preemptively addressed by carefully considering what the reviewers’ misconception is about what your paper is doing, what the other papers about A are doing, and how those two things differ, and making sure to explicitly point out that possible source of confusion and clarify it. For example, you can insert somewhere a paragraph along the following lines:

It should be emphasized that the earlier papers [X, Y, Z] have proposed interesting ways to make A work, as well as reasonable arguments to support those proposals. Thus, it might appear that the current work, which shows that A works under additional assumptions, is superseded by these earlier results. That is not the case; the reason is that the current solution is in fact completely rigorous, and thus demonstrates A under the extra assumptions in a more satisfactory and complete manner than the previous works. Moreover, our formal verification gives further insight into the nature of A that may turn out to be applicable to additional situations, perhaps leading to future results, or even to an eventual completely rigorous demonstration that A can work in full generality.

Summary: at the end of the day, there is always the possibility of getting unfair and invalid criticism, either of a kind that you didn’t expect, or of a kind that you did expect and tried to address preemptively but where the critic simply isn’t receptive to your reasoning. However, the method of preemptively addressing criticism will be able to successfully shoot down at least some of the objections, with some probability. It gives you the best shot at convincing people that your arguments are valid and “interesting for the community”. That seems like the best that one can hope for in this situation. Good luck!
* Source: this is a “principle” that I invented. However, I’m pretty sure I’m far from the first person to discover the usefulness of this technique, so maybe it actually is a principle that was explicitly formulated by someone at some point.