For the last 500 years, the case law has chosen to recognize a "vertical" element to property boundaries. At the elevations we are talking about here (0-30 ft), the vast majority of the case law would support literal trespass by stepping over a corner. And I am not going to google it for you - I have cited one SCOTUS case in the past and there are dozens more readily findable cases and a few decent law review summaries.
As for 5thA -- both you and Pestcontol get it wrong. If an action is a common-law physical trespass, a government easement to grant the access to void the trespass is a "taking" in the vast majority of cases. But of course, the real question is what is the amount of remuneration for such a taking. In one case about running cableTV lines without an easement, SCOTUS found trespass, found a taking, and awarded the plaintiff $1. Again, I am not googling for you or others. The law is the law regardless of whether I provide you case law citation. Feel free to do your own googling.
So we have three simple answers:
(1) The courts change 500 years of case law and vanquish trespass above ground level - if you think this through you can imagine a myriad of unintended consequences outside the arena of checkerboard hunting if they do this, so I prefer that they don't take this approach.
(2) State legislatures pass laws that remove non-destructive, good faith, corner crossing from the scope of criminal or civil trespass law. This is my preferred answer.
(3) The federal government invokes eminent domain to grant recreational "non-destructive" 15 foot wide walking easement across all corners necessary to access federal lands outside the city limits of any town that has a federal post office. Land that actively has unharvested row crops would be exempted. The takings value of these easements will be set at $25 per corner (which is more than the courts will give in most places if folks actually bother to read the takings valuation case law - I am not googling that for folks either). This is my second choice as it does not solve state land corners, but it would be a big help.