They've ruled out hitchiking. Which is a shame, because I'm reminded of the 'Jailbreak' charity fundraiser, where students are challenged to get as far as possible [with sponsors paying per mile] from their starting point using only transport offered for free. Some of them managed to persuade airlines to give them long haul flights...
It is definitely possible to hitchhike with the rule of not walking more then 500 meters. Sounds like a cool game by the way! I loved hitchhiking with arbitrary rules, an entire continent becomes a playground.
Having read the rules, I do believe is is possible to hitchhike in such a way that it qualifies as free transportation that allows to travel the longest distance. A simple way to do so it to get a single ride that is several hundred kilometers long.
The author of the question on StackExchange accepted hitchhiking as a valid answer.