Just winging a WAG, the two lower impedance settings are different taps on the transformer and the 1000 ohm setting is direct drive with the transformer bypassed. That would explain the comment about the 1000 ohm setting sounding better. 1000 ohms is an *easier* load for an amp than a lower impedance, not harder. If the sensitivity is 104dB for 100v, then you should still get 94dB for 10v. Quite a few headphone amps are capable of that. When you run out of voltage, you clip, which is quite audible, and the amp performance should be very good until just before clipping while driving a 1000ohm load. Considering how much compression most modern pop stuff is, 94dB isn't that much of a limitation unless you like your music loud.
If you're a tinkerer, I would think the best amp for the phones would be a headphone amp, not a receiver, with the power supply voltage jacked up to the limit of the weakest parts.
On a class A amp, you would want to dial the class A bias down because the current demands for driving 1000 ohms would be low. Even a Cmoy built with higher voltage parts and
a stack of 9 volt batteries would give you an idea what the phones sound like.