To avoid getting duplicate medals all the time on my ipad (since I prefer playing on it, but the iPhone is the one with 62 missions accomplished), I tried restoring a backup from my iPhone to my iPad, and playing from there. That worked reasonably well, except that I found that there's a bit of copy protection in there: I wasn't able to buy anything after doing the copy. So you can't do a full set of missions after that; you'll inevitably get stuck when you get to the 'buy an item from the stash' mission. Very annoying.
Not sure what I'm going to end up doing about it.