Reverend wrote:

Apologies, that's much easier to visualise than in 2D. For some reason I didn't see that the arcs in the saucer make a staggered loop.
I took the alcoves to be actual stops, I didn't realise they were waiting points. FalTorPan, no need to fret on my behalf, no offence was taken, but thanks all the same. 
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Group hug, everyone!
Just kidding. Everyone but me has cooties.