I very much doubt that it's the impedance that makes the NS1000s difficult to drive in passive mode. With active mode they have a built in, battery powered amp but still have a high input impedance so they benefit from an amp with strong voltage swing. I can just hear audible differences between amps in active mode but it's subtle, with better amps bringing out a hint more detail and making the soundstage more 3D. Current requirement is probably quite low.
Passive mode has lower impedance, so probably not the same requirements in terms of voltage swing. However current requirements are probably not far off whatever's being drawn from the AAA battery used for active mode - maybe even more.
Gain is not much of an issue. I've never had a problem with getting them to run loud enough in passive mode. Taming the bass and bringing out the detail is what it's about. In that respect I think the NS1000s may be quite unusual, hence the number of amps and soundcards etc that utterly fail to run them well.