3 teeth, if it's that loose why would it stop at only jumping 3 teeth, and you'd see the damage to the belt if you looked carefully. Also bear in mind that the TDC indicator can be out, I've seen up to 5° difference between the real TDC and what appears on the crank marker
Which direction is it out by, could you take a photo of the cam gears at TDC?
I'm still inclined to look at the map sensor connection to the manifold, and replace it if it has been tee'd into for a boost gauge. This is what happened to my car not long after I bought it and it had similar symptoms to what you describe.