Thunderbird 350 stopped during acceleration

I think cleaning the carburettor again might be a good starting point to solve this.

Be sure to remove and clean the nozzles,it sounds like your bike gets too little fuel and if the nozzle has reduced flow or is clogged the bike will stop when you open the trottle.

To see if your bike gets fuel you can use brake clean or starting fluid in the airfilter and spray when you open the trottle.if the engine runs with brake clean but not whithout then your bike is starved from fuel.

On top of the carburettor there is a vacum chamber be sure the rubber seal is in the right possition and that there is no air leaks,you need to be sure the carburettor piston moves freely so you might have to clean and lube the parts(piston,spring and the rubber parts),be sure the carburettor piston gets installed in the right possition(it only fits in one direction).