I would figure out why you can't downshift to neutral before i worry about the carb anymore, that could be far more serious. If your lucky its a problem with the shift stopper or the return spring, but i wouldn't ride it around stuck in fourth gear until you fix it, you could end up hurting something else, and using low gear puts a lot of strain on the sub trans, its fine for average use, but i wouldnt ride around on it all day in low gear.. LOL
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....