I think that you are onto the correct parameter but in an indirect sort of way. Damping factor, simplistically, is the ratio of (real part of the) speaker impedance to (the real part of the) amplifier output impedance. Remember that speaker impedance is variable over frequency so DF does not remain 1 fixed #. Unless the power amp output impedance is very low & well-controlled (sign of a robust power supply, which makes the amp cost sky-rocket), the amp output impedance is also variable over freq. So, you have both numr & denr varying over freq! Often you'll see lower DF as you come down in freq (often amp spec sheets show DF at 1KHz) that read in the range of just 10. So, the very large #s you have cited from spec sheets are essentially meaningless - they are probably measured with a non-reactive load (which is not what a loudspeaker is!).
I believe that you improved when you switched to the Karan amp is the amplifier output impedance - I get this feeling due to your comment "Karan took a hold of the speakers and made them play whatever it was sending". When the impedances are correct in the amp-speaker interface this is what the listener usually reports back.
One of the possible reasons for this is that the Karan amp has a much better power supply (lower impedance) & probably has more # of power transistors in the output stage (lower impedance) &/or higher current power transistors (more current delivery capability).
I believe that you improved when you switched to the Karan amp is the amplifier output impedance - I get this feeling due to your comment "Karan took a hold of the speakers and made them play whatever it was sending". When the impedances are correct in the amp-speaker interface this is what the listener usually reports back.
One of the possible reasons for this is that the Karan amp has a much better power supply (lower impedance) & probably has more # of power transistors in the output stage (lower impedance) &/or higher current power transistors (more current delivery capability).