spray baste and a walkingfoot.

HI,
Without really seeing how the piecing was done I offer this suggestion which I just learned from a long arm quilter working on one of my quilt tops. She told me that the binding on the side could make the quilt pucker or in your case place mats. She told me to measure the sides top to bottom and then measure top to bottom in the center. Then average and use that length for your border of your quilt. I could be all wet here but thought I would throw that out. To square up my quilt we took off the side that was too long, cut to the correct size and put back on. The sides of the place mat should be open when you machine quilt then you can finish those off at the end. Hope this helps you with this project or another one in the future. Best wishes to you.