What about the one point on the switch (upper left) that is not connected?
Yes, this is the motor that needed the start switch. My friend ordered one from the folks at Torq and with a little modification to the mounting made it work, at least he thinks so. Obviously he hasn't had the motor running yet.
If it were me, I would remove the motor and bench test it first, without the drum switch, to see if it even works, before spending more resources trying to figure out the drum switch and wiring connections. Looking back at the start switch thread, it was badly worn, and so must the centrifugal actuator part. On top of that you mentioned that the new stationary switch needed to be modified to fit.These thing should be sorted and tested before installing the motor in the machine.
Once you can prove that the motor is functional, then re-install it and orient it, so that the label can be seen. The tag has a connection diagram on it at the bottom, that should be visible, and will also tell you how to connect it it for the bench test. If the motor doesn't start on the bench there is not much use in sorting out the rest, as the motor would need replacing with something that works first, and a new motor will likely be somewhat different in it's connections
If that part gets sorted, then we can move on to the drum switch and wiring.
The drum switch is something you must sort out, to figure out what style you have. The part # you gave didn't return any good results on a search. The picture you provided didn't provide enough detail to see what style it is.
As I mentioned earlier there are many styles that were made. If I recall correctly Furnace made 3 styles that were different. Here is a connection diagram of the 2 most popular styles from Furnace
You study the diagrams and switch and tell us which one you have, then well have a much better idea of which way it needs to be connected. Maybe it's neither of these two, only you can tell.
SAF Ω