We need the pictures, Jeremy. Just use the fifth icon from the left at the top of the Quick Reply window. Browse to find the picture on your hard drive, press Open on your Windows Explorer window, then Add File From Your PC, wait for it to upload, then All Done.
It sounds as if you have a problem with the engine side clutch half, the captive cotter pin was a barely adequate design solution, and it is not unusual to end up with the bore of the clutch half worn and the cotter pin no longer restraining the clutch from moving toward the engine under spring pressure. The cheap and not very good solution is to put a collar of just the right width on the crankshaft so it bears on the upward step in diameter right near the engine, at one end, and on the engine-side clutch half at the other end, thus keeping the clutch half from sliding along the shaft. If the clutch half is still a good fit on the crankshaft it can work reasonably for a few years, but if the clutch half is loose, you will have to replace it. The good news is that the replacement clutch half uses two grub screws at right angles instead of the captive cotter, and it is likely to be a permanent solution.
Please post the long string of numbers stamped on the cooling air cowl of your engine, if it is a Briggs and Stratton. We'll see if we can find a parts list for it, to identify the correct governor spring. (If you have a very early SB45 with a Kirby Lauson engine, we can probably even solve that problem, but we need pictures.)