DoN & John, thanks for your help.

Based on what you've written I have swapped what I labeled as (4,5,6)
with (7,8,9) respectively. With all 9 wires loose and not touching I
rechecked my continuity tests and here is where I see continuity:

7+8+9, 1+4, 2+5, 3+6

This appears to be correct based on your coaching.

The motor shaft is on the right side as I'm looking at it and on the
left of the motor is this attachment that is about 40% of the motor
width and almost the same diameter. This appears to be where the white
wires (that I marked C2 and C3) go.

I checked for continuity between C2 and C3 and the buzzing sound that I
get when making a typically connection was faint (about 25% of the
standard buzzing noise), but it did make a buzz. I'll try to get a
picture of it uploaded and I'll hook just these two up to 240V to see
if I hear a clank noise.