Amplifier damping factor is moot if reactance is involved with the load.
I didn’t say that the amplifier became non linear its current flow through the VC that’s non linear. It’s not the amplifiers fault that the system is operating in a resonant mode with rising impedance on both sides of the box frequency!Our subwoofers also result in a bass image that appears to be part of the soundstage. We build speaker systems where the subwoofers are an intergrated part of a 4-way system, so a subwoofer behaving as you claim traditional subwoofers do would not cut it.
The problems you describe do not exist in a modern subwoofer with a modern class D amplifier. Such an amplifier stays linear irrespective of changes in impedance. There are no resonance issues or timing issues.