Peckish

I agree with Paper Princess. It sounds like you are doing what a lot of people usually do with appliques anyway.

Once I applique the shape on, I turn the block or quilt top over and cut away the background that the applique covers, leaving about a quarter-inch seam allowance around the stitching. That way your quilt isn't too heavy or hard to quilt through.

Edited to add: perhaps trying a different method of prepping your applique might give you satisfactory results without having to deal with pulling freezer paper out?

I used to prepare my appliques with freezer paper. Someone gave me some heat-resistant template plastic (brand name is Templar) and it was so awesome, I never looked back. I can reuse the same piece multiple times, vs. freezer paper which seemed to get soggy with spray starch. The template plastic is see-through, which is awesome for fussy cutting.