Are you using a thread net on the cone? If not, I would recommend trying a good quality thread net.
Also, what is the brand of thread and type? I know that with spools, different manufacturers use different ways of winding the thread on the spool. This is why some spool brands should be mounted horizontally rather than vertically before the thread is fed into the machine. I wouldn't have thought this applies to cone thread, though. That is why my first thought is the thread net.