Perhaps there is another approach, one more direct and which leaves fewer questions in it's wake than does the aforementioned national reciprocity act:
http://www.nationalreview.com/article/443143/gun-rights-reciprocity-constitution
Actually, that approach leaves a leaves a number of open questions in its wake.
While
Shapiro v. Thompson, 394 U.S. 618, 89 S.Ct. 1322, 22 L.Ed.2d 600 (1969), the case referenced in the article, recognizes a right to travel and struck down several laws seen as burdening that right, it did so in a narrow context. The case concerns persons who moved their residence to another State, sought to apply for welfare benefits in their new States of residence but were stymied by state laws requiring certain minimum periods of residency before becoming eligible to thus apply.
So
Shapiro is distinguishable from the usual LTC (license to carry a gun) reciprocity cases in that (1)
Shapiro involves a change of residence rather than transient travel and temporary presence; and (2)
Shapiro involves applying for a benefit granted by the new State of residence under the laws of the new State of residence rather than the recognition by a State in which one is temporarily present of an authorization (LTC) granted by a different State.
The LTC reciprocity issue is more similar to state licence issues in general. A license to marry (as opposed to the status of being married) issued by State A is not recognized to authorize a couple to solemnize and thus enter into a marriage in State B.
Obergefell v. Hodges,
576 U.S. ___ (2015), didn't change that.
Obergefell simply requires that a State issue a marriage license to a same sex couple on the same terms that State issues marriage licenses to mixed sex couples.
In general licenses issued by a State to do something (like practice a professional or engage in a trade) are not recognized by another State to authorize doing that thing. An common exception is the driver's license; and the driver's license issued by a State is generally recognized by other State -- not because it's legally required, but rather because the States have agreed to do so.
Similarly some States recognize other sorts of licenses voluntarily or under certain circumstances. For example, a court in one State may grant a lawyer licensed in another State temporary and limited authority to practice for the purposes of representation of a particular client in a particular matter. And of course some States have, either unilaterally or by agreement with another State, decided to recognize a LTC issued by another State.
The right to travel has some attractions as a basis upon with to argue for broader reciprocity of LTCs. But so far, as far as I know that approach in Second Amendment cases has not worked out too well in the Circuit Courts. I think we'll need both a very well set up case and a significantly reconstituted Supreme Court to have a reasonable likelihood of a sweeping application of
Shapiro to LTCs.