Nim
I like how if you have an error in your calculations, you end up wandering the haunted desert for eternity. Very flavorful.
My solution for part 2 is pretty much the same as for part 1, just modified to work on a sequence of nodes instead of a single node. However, it doesn't find an answer in the time that I was willing to wait for it. I thought about trying to optimize it to run faster, but figured that if it was taking this long on Nim, then interpreted languages would have no chance, so that couldn't be the right approach.
I suspected that maybe the ghosts arrived at the Z locations at predictable intervals. I added some code to output the step count each time each ghost reached a Z (see commented code), and my suspicion was correct. Just needed to calculate the least common multiple of the 6 cycle lengths.