Im preparing myself to get back to construct and the idea, even knowing its probably not the best one, will be to use some sort of ajax to sync things in my game.
I think i wont have that many sync issues you're having because of the game style: by testing your game and checking network on chrome, i think youre polling entire map everytime, right? For this game style (action intense) i think your option would be syncronize every action (every tile dug), triggered by the action itself. Also, as the pace is really fast, the best option would be websockets. Maybe even multiplayer in C2, having a couple worlds preset and state saved, i mean, generating it upon creation only, and then saving its layout.
Sorry if not clear enough.
Also, i really liked the artwork, but i missed a tuto/ gae control info lol.
About the mobile supporting ajax, not sure but i think it works.