I saw Lisa Call's picture on her blog of threads 'hanging loose' on the surface of a quilt.
I also read all the comments to the post and tried out a couple of suggestions. I too hate having to hand thread all those dangling threads by hand AND I hate even more the thread nests that occur when I use the automatic cutter on my Janome.
Oddly enough I saw this advice on another website and found it works well on either machine, both at the beginning and the end of a run - no nests, no dangling threads. Yay!!
Here's what I do - at the beginning of a quilting run, I take a couple of stitches before locking in the row (with lock or back-stitch) then stitch away. At the end of the run, I again lock the stitch, then lift the presser foot and move the fabric away from the needle about 3 or 4 inches and I grab the loose top-thread with my left hand. I then move the quilt back under the needle to the same hole I stopped at. I lower the needle and bring up the bobbin thread, pulling it up from under the quilt to the top surface. I then clip both threads. The results are invisible and the stitch is secure at both ends
Here is a top and bottom pic of this process, done with my Pfaff that doesn't have a locking stitch - so what you see are back-stitches: