It can all be fixed. The body is solid aluminum, not steel. On the backside of the headstock is a Shopsmith nameplate that covers an inspection hole. Yours may have a screw to loosen to rotate the nameplate, otherwise it is held in with spring clips. Maybe you could take a picture through that to see the speed changer from the back side. However, it sounds like you will have to remove the speed changer and replace one or more parts.
Use the following link to see headstock disassembly and cleaning instructions:
http://www.shopsmithacademy.com/SS_Archives/SS122/SS122_Common_files/Blackboard_images/Inspection_and_Cleaning.pdf
Here's a link to the headstock exploded diagram that will should match the part numbers in the instructions above:
https://www.shopsmith.com/service/headstock/headstock_diagram.htm
You'll find all the Shopsmith service parts and diagrams here:
https://www.shopsmith.com/service/mark/index.htm
There is plenty more documentation here on the forum.
Did you get a manual with your machine? I'm pretty sure it mentions the part about not adjusting the speed without the motor running. That is not likely to have caused your problem, I doubt that speed dial was going to move very much at all.