The direction you go does not affect the bug. We go in the most optimal route each time. We do always solve south first now and have not had it bug in the last 4 times we've done pylons. I still think it's just RNG though.
The 4th wheel doesnt matter what side finishes first.
Could be RNG but like your guild, mine always solves South first after figuring out which way we need to click each level. Haven't glitched the last two weeks.