I've used the polar fleece many times on the backs of baby quilts as I like the super softness of it. Granted I quilt on my Pfaff 1473 (almost 20 yrs old)and do straight line quilting but I haven't had troubles with it. I do pin it down pretty close with the jumbo safety pins. Found you have to start pinning in the middle and work your way out...then trim it ups to make it square (well kinda square for me)
On the quilt to the left, it has a "rainbow leopard" fleece (sorry forgot to take picture of it before giving it to DGD.
I've also tied when I used fleece using yarn to match up the colors...don't like the "lumps" from the knots though.
I'm not a great sewer/quilter so if I managed then someone else with better skills shouldn't have too much trouble.
Good luck