With the electric shut off solenoid removed and throttle at Idle, insert a punch thru the opening for the solenoid. See if the linkage pushes in freely in and that the Idle spring returns it as punch is withdrawn.
Here's another vid with me working the rack back and forth more specifically like you described above;
https://m.youtube.com/watch?v=pq_PaL1fOqw
I also noticed that the adjustment screw on the Floating Lever is adjusted way out from what the WSM picture shows. I'm wondering if that was done by the shop that originally tried to fix this.
I tried to screw it back in and was able to get 1 turn out of it but it seems really tight. Is that supposed to be a tight machine fit or is there something else like a set screw or something holding it in place? Its hard to get a good bite on it because the angle I have the flathead screwdriver to get to it.
If you look at this pic -
http://www.orangetractortalks.com/forums/album.php?albumid=567&pictureid=3243 just to the left of the red arrow you'll see the screw sticking out of the floating arm about 1/4". The pictures in the WSM show that screw face almost flush with the surface of the floating arm. Me thinks this could be the problem.
I have to run to a B-Day party for my niece so this will have TBC later.....