I feel your pain! I don't fmq, but have a hq16 that is used with a pc quilter, so the actual quilting is computerized.
Some time ago, I had a terrible time with quilting. No matter what I did, the thread broke or nested or something awful. Finally, I put it all to bed for the night.
Next day, with renewed determination, I approached the quilting problem. It turned out that I had threaded the needle wrong - probably 10 times the previous day, and always the same problem. Once I fixed that, all went well.
Have you checked your tension, upper and lower?
If tension is too tight, the thread will break. I will suggest making a practice sandwich, loosen you upper tension as much as possible, sew a bit, tighten tension a bit, sew some more, etc, until you get good upper tension.
If your machine has a drop in bobbin, I have no idea how to tighten that, or even if it can be tightened.
If you load the bobbin from the front of the machine, then check the tension of the bobbin case. There are numerous you tube video's that will show you how to do that.
If all else fails, get the machine serviced. I got a Janome 1600 for a very low price several years ago and wound up giving it to my sister. She had problems like you describe. She did have a barbed needle, we changed that, but the problem didn't resolve. She took the machine in for servicing. I think that the servicing included re-setting the timing. Once the machine was clean and well timed, it worked perfectly.
Good luck.