My new Solo Ultra Linear

This might be better explained by Graham as I don't understand it 100% myself. But the hiss you can hear is determined by SNR (signal-to-noise ratio) vs load impedance vs electrical sensitivity of the load.

(Impedance matching)

By hiss, I mean background noise produced by the amplifier stage (not background noise in the recording) most audible when no music is playing. Graham has said something very important about amplifier hiss in the past, in that trying to design the electronic circuit to silence it completely will detrimentally "kill" other more important qualities of the music signal so he avoids doing it for this reason. It's a juggling act.

As you say, if there is surface noise with vinyl and background noise in live recordings, trying to totally eliminate amplifier hiss serves no purpose whatsoever and filters don't discriminate between signal and noise so both get attenuated. The designer is spinning multiple plates on sticks simultaneously, trying to preserve the whole picture. It takes a great deal of care and attention to detail.

The Diamond Edition is intended to drive difficult loads like Grados better, with a lower noise floor. You will likely experience a significant reduction in hiss, without any loss of musical qualities. This option will be easier and probably cheaper than trying to calculate component values and buy materials to make a custom cable for the headphone to alter its load/sensitivity characteristics.

I'm confident Graham and other members here would also echo my ULDE recommendation for your intended use.