Just by doing brute force recursion won't even get you up to level 50, I think it's because there are so many choices each move, not just directions like in Runaway and Mortal coil.
Wonder how people got to 1000...
I'm quite interested in whether those top level solutions exploit some specific
attribute of those given graphs or if they do challenge the typical hamiltonian path problem?
Welcome to the wonderful world of heuristic algorithms to tackle NP-complete problems: They may find a solution in acceptable time in the majority of cases, but if they don't find a solution you can't be sure if there isn't one at all, or only your algorithm failed. Here they work very well...