In my opinion the scope, topic and tools of such a paper is just outside of regular scientific literature. In scientific literature it can work as a hoax only. It may work as an opinion piece in an acedemia-related journal, like the news of your field. If you add a commentary and analysis (and possibly you need to cite actual bad papers or a survey on them), it would get much closer to the realm of academic publishing.

Be aware that what you plan to do will cut both ways. The scientifically illiterate public can just as easily interpret your paper as a reason to dismiss credible research. The exercise is not only potentially damaging to your reputation but also to the entire community.

Also there definitely WILL be someone who will take your work at face value and declare that your absurd conclusion is actually The Truth, and that THEY are lying to everyone, etc, etc. And a community will form around your work who will try to preach it as the truth. This has, unfortunately, happened before.

GOD how I miss Martin Gardener!

Not writing this as an answer since it's not what you're asking, but: you are looking for 1) open access and 2) no publication fees. This is known as diamond open access and is rare for obvious reasons. If you know the field of your paper then including this as a keyword in a Google search can easily narrow the options.

It's a shame you missed April 1 by a few days -- putting it on arxiv on April Fools would give you cover to say it is satire, but also make it publicly available and citable. Here's an example of the kind of thing I have in mind: arxiv.org/abs/2103.16583

@psithurism you're not wrong. But actually, I don't think the scientific community benefits from a reputation for being infallible. It's better to risk people denying sound results, than to encourage dogmatic belief in questionable results. Lots of common fallacies started with one questionable paper, if people and the press had done a better job of questioning the Wakefield paper we might never have created anti-vaxxers.

Publish it anonymously, it will not matter where you publish it.

@A.I.Breveleri As good as his gardener may have been, Martin Gardner is even easier to miss :-)

GOD how I miss Martin Gardner!

look at this paper: jstor.org/stable/… The Spatial Distribution of the Montane Unicorn was published in a top ecology journal

Have you also considered publishing the paper on a blog, or making it into a video presentation which links to the paper?

Social Text?

Frame challenge: make a serious, formal paper about misusing and misinterpreting scientific data, and use your "parody" study as part/demonstration of it

@Andrew here's another one: https://arxiv.org/abs/2203.17060

You might wish to read up on and take note of the publication history and venues of Isadore Nabi.

In cryptology, there used to be such a journal - the Journal of Craptology! It published a paper very like the one you've written - the marvellous Cryptanalysis of Caesar Cipher by Malgorzata Kupiecka.

And GOSH how I miss Martin Gardner!

"It would like it to be published in such a way that I can tell everyone it was accepted by ""prestigious and well-known journal XY"" (regardless of whether the journal is really prestigious)" - isn't it how predatory journals work?