I see no logical link between an action being licensed in one State being forced to be accepted by another and the P&I clause. The courts have ruled that the clause applies to rights that are "in their nature, fundamental; which belong, of right, to the citizens of all free governments; and which have, at all times, been enjoyed by the citizens of the several states which compose this Union, from the time of their becoming free, independent, and sovereign."
That which is licensed is, by definition, not such a right as described above.
The P&I clause exists so that one State may not allow all of its citizens free exercise of religion, but deny such to citizens of another State. There is no logical argument by which this clause can used by the feds to insert themselves into the recognition by one State of another State's licenses.
One might argue that it should not be licensed, but freely allowed, in which case the P&I clause would apply, but reciprocity of licenses would be moot. However, once you accept that the act may be licensed, you are agreeing that the act is not a right under the P&I clause. So, either the P&I clause is either moot or not applicable. You can't have it both ways.