Bryan,
My 4700 did this as well. I had to take off the panels around the fuse box and I think the green one as well. But I was replacing the dashboard glass at the same time so maybe you won't have to take as much apart as I did. On my the black fuse box panel fit over a bolt. The fit was VERY tight. I had to very carefully pry the panel off with long screw drivers. Then I made the bolt hole larger.
The throttle linkage just needed tightning. Took a minute or so to fix it. But took a good hour to get to where I could fix it.
I ran with the loose throttle for years. I mean years. What did I do to keep the throttle in place? I created a TPW, aka Throttle Position Wedge, which is a piece of cardboard, maybe 2 inches square, wrapped in the mechanics friend. Duct tape.
Put the throttle where you want it, and push the TPW in the throttle slot and you are good to go.



When done with the tractor, pull the TPW, slow the RPMS down, and put the TPW in the fender box for next time.

I think I wore out one TPW and had to make a second one.
Later,
Dan