If you're still interested in this, Tom Davies (Geowizard) has done the straight-line crossing in a couple of different countries and posted videos, both of some of the planning and logistics and of actually doing it.

Two of the most relevant are walking all across Wales in a straight line (which did involve trespass on some farms) and dribbling a soccer ball the entire length of the Hadrian's Wall path.

He calls these "straight line missions". Maybe it will inspire you to try some form of this sport, or maybe you'll just enjoy Tom's experiences.