I think Thimblebug's suggestion is the best one in this case. The problem here is getting off the paper once you've sewn over it, not just the "normal" amount of effort it can take to remove it. Once you get an area to put your finger under you can probably run it around to loosen it and may be able to carefully tear away the paper.
While I do use parchment paper for quilting designs, I've never sewn through freezer paper, it is so thick! In the future I would probably make sure the freezer paper doesn't go into the seam lines. There are other alternatives too, like wash away iron-on stabilizers.
And just as a reminder because I'm big on these things, change the needle before your next project. Sewing through paper does not make them happy!