I think I finally found a WordPress setup that allows me to use Markdown for writing posts, both in the browser and on my iPhone/iPad using the WordPress iOS apps.
A combination of two plugins:
The first plugin makes it possible for WordPress to save posts in Markdown format and display them on the front end. The second plugin replaces the WordPress rich text editor with a Markdown friendly toolbar. I even used the "Markdownify" setting that came with Quck Tags to convert my older HTML posts to Markdown in the database.
The whole setup works flawlessly!
If you write for the web, I highly recommend checking out Markdown. Once you get a hang of the syntax, it makes writing easy-to-read and easy-to-convert-to-HTML text a breeze.