I’ve quilted Queen sized quilts with Minky backs- it is my families favorite quilt back. I do use batting between the Minky and the quilt top. It’s important to Smooth, not stretch it. If it’s all basted it’s shouldn’t be stretching. Loosen your tension just a little, I usually use a 50 weight thread, but have used 40 a couple times. Make sure you are using a nice, sharp, new needle.
ive not had the ( bearding) problem, maybe because I use batting- which seems to hold everything together nicely. I have heard that the fibers go back where they belong after laundering. A thinner, sharp needle might help.top tension needs to be a bit less too.
maybe ( if you have any extra) put together a couple small sandwiches together and practice a bit to get the hang of not stretching your fabrics,