I've only made one quilt with minky backing but here's what I did - my backing was just barely bigger than my top so I heavily thread basted it to the top and sewed a muslin strip around the perimeter of the quilt. I loaded it on my long arm like that so there would be no stretching or bunching. It quilted up just fine and after I was done I cut off the muslin when I trimmed it up.
Cari