As you know, it all has to do with amp/speaker matching and I don't believe the Sphinx can deliver enough current into a low impedance load.
My understanding is that high current amps produce a stable output of power that is coherent across the amp's impedance range
Yes, that's true, but what if the speaker load is not stable? An amp that delivers high current can drive low impedance spikes in the bass frequencies with authority, and will have plenty of reserve power so that it does not go into clipping. There will be no distortion and the speaker will sound more dynamic.
It will handle transients at all frequencies with power to spare.
An example of a high current amp is one that can double it's power from an 8 ohm load to a 4 ohm. e.g., 300wpc/8ohms, 600wpc/4ohms.
I don't think high current and damping factor are related, any well designed amp can have a high damping factor.
A driver with a voice coil is in a magnetic field and for each motion, the coil generates current to the amp. The damping factor is like using the brakes on the voice coil and driver.
Jim, you don't need an amp that doubles it's power to drive your new speakers, but you do need a bigger amp, at least 200wpc.
I've always owned separates, but maybe look for a used Music Fidelity amp.