What source have you been using with the NS1000s?
Given the difference in sound signature with ANR on, I wonder if an open headphone might do the job? I love the NS1000s sound but it's the lush airy mids, detailed treble and punchy bass that I like are not especially characteristic of closed headphones. The bass has impact but doesn't really go that low. With ANR on it's all exceptionally well controlled - and that makes them very good for capturing soundstage information inherent to the recording (as opposed to a headphone adding its own 'headstage').
The control comes not so much from them being Noise Cancelling, I think, and more from inclusion of an amp within the headphones that is very well matched to the drivers. The nearest I've heard in a closed non-noise cancelling headphone is the Audio-Techica OX7AMP - which although not noise cancelling does have a somewhat similar design to the NS1000s (with a built in amp, requiring an AAA battery). Unfortunately they are also plastic construction - so perhaps may face similar long-term durability issues to the NS1000s.
But having said that, most of what I like in the NS1000s (ANR on) in terms of sound signature is also done well (but better) by the Sennheiser HD600s. Don't get me wrong - they are a very different headphone but they capture soundstage information inherent to the recording in a similar way (without addind anything of their own). But once again, like C64's comment on the Momentum's, they are simply a better headphone than the NS1000s, not least in build quality. They have that wonderful midrange presentation that captures human voices so well. The treble lacks the 'sparkle' that the NS1000s have but it's a more natural sounding presentation and the detail is still there. But they do need a suitable amp and source to shine, they're not exactly portable. And unfortunately - at the moment - I can't see many available under £200.