When I EOC I only turn the key back one click (from "on" to accessory) and when the engine dies I go back to "on". That way you accumulate almost all of the miles you actually drive, and at least in my car I still have power steering. So yes, the key is in the second position, dash lights on, while I EOC.
I haven't really played with tire pressure yet, though your results make me exited to try, especially the part about longer coasting