Hi!
Your analysis is perfect!
In Settings->Reading, WordPress resets the page_on_front option if you choose to display posts. And that's not the case in Customizer. As you wrote, it is not consistent but I have to deal with this as WordPress does it (i.e. systematically test show_on_front before testing page_on_front).
So the current development version (1.5dev31) should fix this.
http://downloads.wordpress.org/plugin/polylang.zip