I was hoping you would get a definitive "for sure" answer, because I am having sort of the same problem. But my machine just won't pick up the bobbin thread when I have the darning foot on. I did knock it out of alignment and when I got it back from the repair shop, it wouldn't FMQ. Getting ready to take it back to be looked at again.
But I was wondering, on yours, if there could be a problem with the spool allowing the thread to advance? Or if it gets hung up? Mine advances so hurky-jerky with the FMQ foot on, it sometimes flops out of place and gets wrapped around something that holds it firm. I know that's not right, either. In the past, I have had thread get caught by a burr on the edge of the spool.
I hope you find out what's causing it, and can correct it.
Oh, and you might check with your quilt shops and machine shops. I bet they know someone local who works on all kinds of machines.