You don’t “have” to buy seatalk jumpers. Just need three wires connected same to same. I.e.red to red, yellow to yellow and screen to screen.
I think you have it worked out now.
On my autopilot if the autopilot is on and connected to other instruments that are not powered on you will get a seatalk failure message and it’s unusable. That is the only reason I can think of.
In your arrangement though it really should have been wired to wind so the autopilot could sail relative to wind (trim) as opposed to holding course.
Based on previous photos and your diagram, and memory I think you are currently wired as marked up.
The wires in the lower right of your diagram should be to power.
As you’ve noted I think as wired on page 11 might give you the options your looking for - although it does require all instruments to be powered up in order for your autopilot to work.
By the way - looks like you should be able to do the Garmin nmea connection either at the course computer or at the control head. Will give your autopilot course, waypoint, crosstrack error etc.