Okay, you've tried a lot of things. The question is this: is the thread snapping (where abouts in the path), or is it shredding at the needle? Here are a few more:
Remove the top thread, ALWAYS RAISE the presser foot, and rethread from the beginning.
Try different thread--perhaps a polyester thread like Isacord or Aurafil. (AVOID old or bargain bin thread.)
Try a different kind of needle (brand new needle!)--like a top-stitch, microtex, or embroidery. The top stitch needle has a larger scarf that will better protect the thread if shredding is the issue. (I use a special bobbin case that I've increased the tension for Isacord thread and I use the same thread in top and bobbin.) I also decrease the top tension a tad so the bobbin thread will not pull to the top. You may need to install brand-new needles several times on one quilt when they get dull.
Usually an 80 or 90 needle will work for FMQ through a fabric/batting sandwich.
Check that the needle's eye is the appropriate size for the thread (also a cause of shredding thread).
Set the upper tension at the midway point perhaps a bit looser for FMQ (this tension will probably need to be tweaked for your particular machine due to wear and age).
Use an FMQ foot and drop the feed dogs. A Supreme Slider (avlb on the internet) is very helpful in helping move the quilt while doing FMQ.
Work at a moderate but steady pace. I find a faster speed while FMQ gets me into trouble...like spots I can't get out of, overlapping stitches, or outside the quilt edge.
FWIW, I still get some skipped stitches with FMQ. Usually, it happens when I move the fabric too fast, especially around a curve. I have a tendency of speeding up while going around a curve that will cause skipped stitches or eyelashing.
I'm also wondering if there is something to do with the fabric and/or batting you are using...like is it Batik? Batik is very tightly woven and presents some particular challenges. The type of batting could be more dense, making it harder for the needle to penetrate the sandwich. Also, pulling or stretching the fabric can cause skipped stitches.
Basic Maintenance Tension Skipped Stitches
Here What to Do if Your Sewing Machine is Skipping Stitches
10 reasons for skipped stitches
If you see no improvement in your machine's stitching, you may want to have it serviced.