I ran out of editing time so here are some more photos:

The fan before (top part):
[Linked Image from s28.postimg.org]

The fan before (bottom part):
[Linked Image from s24.postimg.org]

More fan detail:
[Linked Image from s12.postimg.org]

The rusted remains of the capacitor and transformer:
[Linked Image from s13.postimg.org]

The rotary selector switch (2 pole, 5 position):
[Linked Image from s15.postimg.org]

The name plate and switch backing plate:
[Linked Image from s27.postimg.org]

The start and run windings:
[Linked Image from s15.postimg.org]

My understanding of the circuit diagram:
[Linked Image from s12.postimg.org]