If you really want to write for the public, consider trying to write "popularizing" articles for magazines/newspapers/websites that the public reads. There's definitely a market for well-written articles that explain new discoveries -- or even old discoveries, interesting techniques, and basic principles -- on a level suitable to someone who is science-literate, generally curious, but not deeply steeped in your field.
Scientific American used to have magnificent examples of this kind of writing, though my perception is that they've gone downhill in recent years. Technology Review magazine often has good examples, though they're obviously biased toward articles contributed by the MIT community.
Steven Jay Gould's extended series of essays in Natural History magazine were a great example of explaining fairly subtle aspects of science -- and of the history of science -- in near-layman's language. Anthologies exist covering just about the entire run -- including pieces where he corrected his own prior essays when new information became available.
As a much older example of the scientific essay form, Berton Rouche was just about synonymous with the "medical mystery" form, in which a puzzling (preferably real) case is presented in semi-story form, which is then used as a springboard to discussion of the biology, chemistry, history, diagnostic technique, or whatever else the essay is really about. Most of his pieces were originally published in a magazine (the New Yorker?) but subsequently collected into anthologies; it shouldn't be too hard to find them and they're fun reading if you're a scientific omnivore.
Of course those two were excellent writers as well as having scientific knowledge. I'm just suggesting that, if your focus is on the public, that's the kind of ideal you might aspire to. You'd need to be able to write well and clearly, have something to talk about which they'll find interesting (or that you can quickly convince them they should be interested in), and be able to discuss it in terms of things they're already likely to have at least some knowledge of (or be able to define your terms as you go without losing the reader along the way).
Of course as with any kind of writing, don't expect it to come quickly or easily. Popularizing articles are a craft of their own, the market isn't huge, expect to see lots of rejection letters unless you're "self-publishing" onto the web (fewer as you hone your craft)... all the usual platitudes and advice about writing for the public apply.
And as Gould demonstrated, this can be done alongside a productive research career producing results not immediately accessible to the public. Doing both simultaneously is a lot more work, but it's one way to reconcile the conflicting goals of advancing the field and advancing public knowledge about the field.