I don't really know. I've seen a few kits that required moving wires but they had instructions.
The motor is pretty simple. It only has two windings, start and run. Start ohms out higher usually. You know which wires run through the centrifugal switch so you can ID them. On the motor side the blue wire is probably the start winding as it runs through the thermal safety.
If I came across this on a service call I probably leave the wires in the terminal block of the motor where they were as long as they were connecting with plugs that had wires on the harness. And I would try it.
GE makes theirs a little harder to run open because of the belt switch but you can try it all live by just rotating the front panel away and leaving the door switch attached. I don't like to work on them live unless I have to but in this case I'd say try it and if it doesn't run normally or trips the breaker then worry about it.
You can try to use the wiring diagram to ensure that wires are going to the appropriate windings. GE makes a pretty light wiring diagram. There's just not much detail.

Well then. You've got a puzzle.

Start with the motor. Ignore the wire harness for now. I wish I had a better answer as you've invested a lot of time and $. Here's how I'd start. I've never had to go this deep on a motor, odd as they usually drop right in. But here we are.

ID what motor terminals are the centrifugal switch. That'll eliminate 2 wires. It'll obviously be the pair that closes when you move that arm.

This is how I do it on compressor motors if i have doubt and i think it'll be the same. To ID motor windings ohm out the remaining 3 that go into the motor itself. You'll get 3 readings: the highest is across the 2 windings, roughly the sum of the other 2.

So say you get 3, 6, and 9 ohms. 3 and 6 are your windings, 9 is across them. So when you see the highest reading the odd pin out should be your neutral, it may be the one that goes into the thermal safety.
I'll see if that test actually works on a dryer motor Wednesday if I have one to test. It should. I think I have a Samsung motor with a bad switch waiting for recycling.
From there you can use the schematic to see which harness wires go where. The comp!ex part is that the harness plug is used as a junction as well, which may be marked elsewhere on the paper schematic and the wire colors may change. Its just how vague the schematic is.
You must think like me to have gone this far. I like figuring this stuff out. Call me a masochist or maybe just too damn stubborn to let a simple thing win.