What does the absence of passive margins between 1740-1600 million years ago tell us about the tectonic environment at that time?
Good paper you reference there.  I think you are starting to answer some of your question by noting that Bradley associates the absence in passive margins with the Nuna supercontinent.  All "rifting" / spreading is taking place in the oceans - pretty much a requirement for supercontinents,  and in this case all continental margins (or at least for those with surviving geological record) were destructive margins.  Over time the duration of passive margins has changed.  For more recent supercontinents you mention, the shorter cycle of a passive margin may have made it very unlikely that tectonic events could cause a simultaneous gap in all passive margins.

As Bradley points out in his conclusions, tectonic activity when Nuna was around may have been globally more sluggish that today, or during the time of Rodinia and Pangea. It may also tie in with the formation of some mineral deposits.  For example, there is a peak in porphyry deposits at about this time.  Now taking into account that older porphyry deposits are less like to have survived (lost through erosion, buried or consumed in later tectonics) the peak at this time may reflect that it was a particularly good porphyry generation time for so many to have survived.  Porphyries do like convergent margins and there would have been lots of those.