We already have federal reciprocity: it's called the 2nd Amendment. I think the full faith and credit clause also guarantees national reciprocity, or should.
Getting the federal government involved does have risks, but if it's done right I think we're better with it than without it. Being done right though is questionable I agree. But if the federal government makes a law reinforcing the right to bear arms guaranteed by the 2nd Amendment, and makes all states obey the law by recognizing the permits issued by other states to exercise the right, we would be better off than without such a law. Ideally no permit to exercise a Constitutional right should be necessary at all. But as long as we have that, at least all states should recognize all permits. Any federal law should begin by stating unequivocally that there is a Constitutional right of law-abiding citizens to bear arms, that the right includes carrying concealed weapons, and that no state has the authority to deny that right to the citizens of the several states.
This might not necessarily be the best way, but we should be working toward making all states obey the law, because states disobeying the law with impunity weakens the law.