Sorry dude but does that mean you've put the original carb back?
Any new carb will NOT work out the box.
I'm slowly steering towards you taking it to a Vespa mechanic to be honest.
1, use only the original carb, 99% sure nothings wrong with it.
2, your choke melted it's cover, that does need replacement.
3, Did you check the throttle cable I mentioned as it enters the carb, the U bend bit above the carb.....have you got it directed towards where the cable naturally comes from. If it's forced round at an angle it could bind and cause open throttle
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