Do you have second every time? And is it more chunky clunky than before? Wondering if your problem is shift drum related. Sounds like it could be a bent shift fork or maybe the spring that returns the shift drum to center is stretched and doesn’t get the shift fork out of one trac before going into another. The pins that go into the shift drum could also be worn.
Is the place the clutch cable pulls on the arm on the same side of the engine as the clutch? From the diagram it looks like the way it works is the whole shaft gets pulled when you disengage the clutch. That mechanism could be worn too. Sorry to say that your best bet is gonna be splitting the cases. May the moped gods take pity upon your soul.
Mind you this is all spitballing from wrenching on Hondas. You’re probably more qualified in this department than me 😬