Since the problem is on the return flight only (correct?), one option would be to just ship your pistol back to your local FFL before leaving MT. Just verify with the FFL that he's amenable to that arrangement.
The NPS isn't particularly gun friendly. If I remember the genesis of the legislation allowing carrying firearms in national parks, the Park Service "countered" with a regulation saying while carrying was legal, it was generally not legal to discharge firearms in parks. Also, the "not in facilities" apparently, in some parks, extends to park buses, ferries, etc.
And state laws still apply. And if you're thinking about continuing into Canada from Glacier, read through the requirements there: https://www.thoughtco.com/laws-for-t...canada-3321846
Beautiful drive, as @RJ noted.