Sewer's Aid is a liquid that re-hydrates dried out thread. It works wonders for me when machine quilting.
If you didn't find any rough areas with the dental floss, I'm thinking the thread is rubbing somewhere. Can you try running the machine on scraps but watch the thread instead of what you're sewing or have someone sew while you watch the thread. Track it all the way from the spool & watch for the fraying to start somewhere along the path.
I have had mine fray on the side of the hole on my straight stitch foot and plate. I had to move the needle just a smidge.
Take the stitch plate off and look on the bottom side of it to see if there is anything near the hole that could cause fraying.
With the stitch plate off, Needle down and see if there is anything touching the needle or thread on the way down to the bobbin. The needle should be a couple hairs away from the bobbin hook but not actually touching it.
You haven't dropped your bobbin or bobbin case recently?
Did you say this was on a quilting frame or not?