I have the 440 QE with the BSR and have not had the problem you are having...mine would suddenly have a big stitch if I moved it way too fast. If the needle goes up and down several times with out making a stitch it would seem to me that the needle may not be delivering the top thread down completely, so the bobbin hook can't catch it, and no stitch can be formed. If it does fine with the quilt sandwich and the sandwich is a little thinner than the quilt, that would make sense, especially if the needle was not inserted correctly, threaded correctly or if you have the wrong size needle (am thinking that a too short needle wouldn't penetrate the thicker sandwich adequately). You have said you cleaned it, but I suppose a piece of lint or thread could obstruct the thread. I am not an expert at this, but I do understand your frustration. I do feel that it is something that can be solved by taking the whole thing to the dealer as you mentioned. My Bernina can be fussy with certain threads, but lately I have been using coates and clark when I only have the color I want in that brand. My dealer recommends guttermann, but I have used mettler with no problem. When FMQ on my DH's Christmas quilt, I used Superior's Bottom Line for the bobbin thread and I really liked it. Oh another thing...I believe that when I took the BSR course, they said to reduce the presser foot pressure to 1. Don't despair, I am sure they can help you figure it out.
Just curious, does it do the same thing on both mode 1 and mode 2?