I haven't seen that one but I do have the Silent Rider ATV silencer for my yamaha Grizzly. - Amazon
It works well and I use it when I take the quad out and do a hayride, to keep it quiet. You can see it in this picture:
Silent Rider
yes, someone told me that there are sbowmobile and atv trails with a trailpass you can get, but that was a while ago. I have my quad registered and insured in NYS but they'll impound it if I drive on the roads.
Blue smoke is a sign of oil getting into the combustion chamber. Could be seals, rings, or other oil through the intake.
How is your air ruler, is it oil soaked?
I think I did read somewhere people were replacing the shift shaft, not sure. The clutch was my first guess. Can you get it in gear when on the move or is this just stationary shifting through the gears.
Go this site and look up a frame schematic. There are a couple of choices that year for the 350 2WD Big Bear. Maybe there is a difference. https://www.rockymountainatvmc.com/oem-schematic/0
Unfortunately I don't know much about that brand but I would look to see if you have a coil, and ignition module, or relays that control the ignition. Do you have a manual?