The choke on my 350 doesn't stay out. It's kind of annoying because it takes two hands to start it. What piece makes the choke stick? I probably need one of those.
I have never been into the handle bar part on mine. I would bet the problem is with that spring. Especially since it sounds like the choke is working. On the 660 I worked on, the choke was stuck. I think cable stretching was what made it seem to pull back.There is a spring behind the elbow where the cable goes into the carb, check that one, and the one in the handlebar assembly aswell.