I've tweaked and fiddled a bit, and now have a satisfying version of my website for mobile browsers. It all should just work, with a link to the full site on the top right should you prefer that.
I still want to tweak the layout, the pages list only shows up at the home-page, where it maybe should show up everywhere -- navigation matters. Also the search box shows up at the bottom, but maybe I should move it to the top.
I've added the little snowman to the home-page at least, to sync it with the main site's design.
I have also tried to keep it small. It currently loads at a 135kb for the main-page. Looking into making it less KB (the full version consists of 1MB of files, also trying to make it smaller). Just because a lot of us have fancy speedy connections doesn't mean I should aim for that. I aim for the average speed and hope it doesn't take too long to load either page.