The last thing you can try is to swap the fans (with the control pins) in your printer.cfg to see if the heatbreak_cooling_fan is now on continuously and you can control the hotend_fan:
Have read a bit about the problem and creality ender 6. Apparently the hot end fan is running constantly on this model. It has a small circuit board on the top right back of the printer, where stepper motors etc. are connected, then a wide cable runs down to the mcu at the bottom.
This small circuit board is feeding the fan power all the time.
Maybe you can disconnect it from that board and extend it down separately to the bigtreetech mcu “hot end heat sink fan” port.