The one slender bit of hope came from Justices Alito and Gorsuch, they contend that the absence of clear indicators in the NYC policy of when a person could stop their "journey" which is similar to the way NJ punishes folks using FOPA to transport firearms across their borders does constitute a non-moot issue. In addition, they support allowing the plaintiffs to amend their complaint if necessary to examine whether the policy has damaged members of the NY State Rifle assoc by revocation of permits in the past or prevented them from traveling in the past to their detriment. It is possible that SCOTUS might send the case back to the trial court for reexamination under such a case.
One thing that is probably holding Dred Justice Roberts in check is the potential that a couple more justices might be appointed by Trump in the future, he has to remain in good standing with the conservative bloc to retain any power whatsoever. However, if that threat is removed or alleviated by a new Dem. president, then Roberts appears quite content to let the 2A wither on the vine.
Thus, he might throw half a bone to Alito, Gorsuch, and Thomas, and probably Kavanaugh by not outright killing the case by mootness but remanding to a lower court to examine the issues of damages and perhaps the vagueness issue of the new policy which would make the case non-moot.