The quilt is beautiful Cinnya! I love your colors
I do not know what to tell you, I've used Minkee and fleece for backing baby quilts with no problem. I used lots of safety pins. It seems to me that fusible web would melt or flatten the fleece. I learned the hard way (with my very first quilt), that hot irons and minkee are not made to be in touch with each other = )
So, what are you going to do now?
Sally