Please recall that there is already an act, that dates from the late 1800s I believe, that gives the FedGov title to the land within a stated distance from the actual border and is only in doubt in a few places mostly in Texas and New Mexico where deeds were granted prior to the act (and in some cases prior to the settlement of the border lines). No easement necessary, just exercise existing authority. Adverse possession not an issue because no Federal property tax, so they can't be said to have been paying taxes on the land in lieu of the deed holder
As I said, if it's private property, and not in an easement, then have at it. Godspeed. Do your thing. Just pay for it privately.