I now resoldered the litz wire from the voice coil at the terminal area, and have also applied a music signal directly to the woofer, outside of the speaker cabinet. I think it is more difficult to judge the distortion when the woofer is outside the cabinet, but outside the cabinet and already at moderate volumes, the woofer starts to sound bad, almost like a cone breakup.
No visible problem with the spider and no voice coil rub.
Tomorrow I will try the woofer in the other speaker cabinet to see if there is a difference.
Could the problem be related to a bad crossover capacitor?