DR Cillaliz - Hmm... Is the grill pan you have cast iron? If so, has/is it already seasoned? If not, well... Next time... semi-generously oil the pan before putting on the heat. And then let it heat up over medium-low heat for a few minutes before turning it up to medium/medium-high. And, yes, it should smoke a little. Then just to be safe, I would place a little more oil in the pan.
Now, if your pan is not cast iron, well... The general rule - which I remember from Jeff Smith, The Frugal Gourmet - is "Hot Pan, Cold Oil - Food Won't Stick". Let the pan heat up first, then put the oil in.
As for "the turning", well... I'm guessing the sugar from the applesauce and maple syrup probably contributed to your sticking problem. Otherwise, once enough of a crust has formed on the burger, it should more or less release on it's own - well, with a little bit of help. I would also lower the heat a little bit - turkey meat, especially when ground, requires gentler handling than beef does. But then again...
Stick Happens.
