I have two suggestions for you.
1) For books, authors are encouraged to submit a "proposal." Here are some sample instructions:
Please be sure to include the following items in your submission. Your proposal should not exceed 30 pages and should preferably be in the form of a Microsoft Word document.
A title and a subtitle.
A one-paragraph overview that explains the premise of your book, why you wrote it, and who you see the audience being (with any relevant demographic data you might have about the potential size of the audience).
A brief author biography (1–2 pages) that focuses on why you are uniquely qualified to write your book and what kind of platform you have to reach a wide audience.
A table of contents that outlines the book, with chapter and section titles, as well as brief descriptions of the material each chapter and/or section will cover. It should be no more than ten pages total.
A market analysis of the potential readership for your book, including a comparison to similar books. When comparing your proposal to other works, please briefly explain (just several sentences) how your proposed book differs from these titles. Please limit yourself to 3–4 books.
A sample chapter that is representative of the style and content of the larger work.
I will suggest that you take this as inspiration for how to pitch your article to journals. Try to reduce the 200-300 word pitch down to a more manageable size. Maybe your pitch will be a little bit longer than the sample I included. Imagine that you are writing to someone you know pretty well in one of these near-fields. Explain to this friend why your article will be interesting to its target audience.
Interestingly, when I have gone through this exercise, I have ended up with a clearer idea of what I'm trying to accomplish with my article, and it has enabled me to improve my article!
Your pitch may be a bit different depending on which area the journal you're submitting to covers. For example, if you submit to a chemistry journal, your pitch would be different from a submission to a physics journal. You would need to explain to the chemistry journal why your paper would be interesting and important to chemists. And for the physics journal, why it would be interesting and important to physicists. (Physics and chemistry are just examples.)
The pitch is written in a more down to earth way than the paper itself. And note that the pitch is not the same as an abstract.
The pitch is kind of like those short blurbs you hear as ads in the Fresh Air podcasts, where the advertiser tries to give you an idea in 25 words or less what kind of book is being advertised, so you can form a very quick idea of what kind of book it is.
Your pitch will function as a pre-submission query. As others have noted, this is unusual. The better you can prune this down, and really focus it, I think the better your chances will be.
If you are going to introduce a completely new animal to your circus, you need to describe this animal to people, so they will be receptive to it.
2) Find at least one person with a strong publication list of his or her own to put in a good word for you -- in whatever way that person is comfortable doing. In other words, do some networking. This person will not be recommending that the journal accept your article. Rather, this person will be requesting that the journal seriously consider your submission, despite its unusual nature.
Make sure that you and this person (~mentor) are on the same page about the thrust of your pitch, so that s/he can underscore some important parts of it, in a way that matches your description.
Last note. Please don't be tempted to start with the first paragraph of your question here, or anything like that. It was fine for Academia SE, but it wouldn't be an effective way to start your pitch.
To clarify, adapt the above sample instructions to suit your needs. Specifically, I would enclose the manuscript itself along with the thing I have called the "pitch."