IMHO that's not making Moodle more readable on a smaller device.
The first thing to do --whether you're looking for a mobile theme or not -- is to use a two-column layout, and put the sidebars on the *right*, not the left. Also avoid a heavy/tall top banner.
Real-estate on the top-left is especially precious on mobile. You don't want to waste the top with a header, to avoid making the reader scroll down all the time.
And, if you want a class to be able to read course content without continuously scrolling to the right, you don't want waste the left on a navigation panel, which is something they need to get *to* the content, but after that they leave alone.
There *are* Moodle Themes with a two-column (versus three column) layout. And there *are* Moodle themes that put the sidebars on the right. So look for those. NB: there is a "Multilayout" theme I haven't tried, but most Moodle themes seem to plan the layout for you.
Just stick to the ones that are most efficient for top-left and the "white space" design issue won't be such an ... issue.
However, once you find your theme, and the layout is "clean", you can make minor changes to a variant of that theme in the CSS and reduce some of the white space if you want.
I use the "brick" theme (http://editconsultants.net/moodle/course/view.php?id=10/?&theme=brick) and did some work on its margins and white space (as well as of course changing its colors and banner) to meet these requirements. I am not a professional designer, and it's not terrific, but we're a public school system . I will attach a side-by-side comparison so you can see the very subtle spacing mods.
HTH,
>L<