Hey Marion, I was having problems with thread shredding on my Sweet Sixteen while using sulky sticky fabrisolvy. I finally realized that my needle was getting gummed up and that was causing the shredding. It may be that your fusible is causing some buildup on the needle that then creates friction on the thread which leads to fraying. In my case the solution is to carefully watch my needle for signs of buildup and remove them- I use my fingernail or one of those alcohol prep pads and do it while the needle is still in the machine and threaded.
If that’s what is causing your shredding issue you will see it on your needle.
There are anti-glue needles for domestic machines that can help prevent the problem.
Rob