Until we get an affirmation from SCOTUS that the 2nd A is an individual right, that's a very uphill battle. And even then, landholders have the right to restrict weapons on their premises - a bar, for example, can prohibit guns. So the NPS could probably just say they were restricting guns as a landholder (I'm not agreeing with them, just debating the point).
Private landholders, yes. This is "federal property", and as such subject ot all the Constitutional provisions and restrictions. Ie; no legal restrictions can be placed on firearms carry.
Period.
If you are waiting on someone else to hand you back your Rights, you are not only thinking about your Rights the wrong way... but you are going to have a LONG wait ahead of you.