Put the shuttle carrier shaft in the bushing and see if it wiggles. Is so bushing is worn and needs replacing. bushing are pressed in. My late father came up with a way to remove the bushing a with a nut, bolt and big washer. can remove old one and replace with new one with those 3 items. The shuttle carrier should just turn in the new bushing with out any wobble.
To take the long drive rack out, there is a connecting screw in an access hole in the back. Screw #89. That release the long wrack. I normally have to pull the replaceable horn to replace the drive rack, The teeth on your drive rack look go. Chances are wear is in the drive pinion and the following pinion. I will also tell you the bell crank is probably worn as well. To replace that you have to take the end of the head off. 4 screws hold it on. You also have to drive the piston pin that connects to the needlebar out. It is a tapered pin that drives out from back to front.
glenn