Sounds like several DIFFERENT problems goin' on.
For the fuel not shutting off while sitting - the petcock is leaking thru. Rebuild, replace or splice in a manual shut-off valve (as from a lawnmower shop) in the line.
Also, the carbs' needle valves are not shutting off. Go thru them again and check for debris, damage to the needle tips, damage to the needle seats. Repair or replace as needed.
While you're in the carbs, check / reset the float levels. One or both may be set too high, trying to flood the motor.
As for the losing power and shutting off, that could be minor, like carbs just starving for fuel (trash in lines, etc) to gas tank not venting, etc. Or it could be major, like the motor is trying (and succeeding) to sieze due to incorrect oil/fuel ratio, overheating, etc.
I'd fix the carb fuel shut-off issue first, including float level, etc. then tackle the possible siezing.
For a manual, perhaps someone over on the VJMOG forums could help. Quite a few fellows in the Suzuki sub-forum with the early two-stroke twins.
http://vjmog.com/forums.htmlGood luck, and post some pictures of the little gem if you can.
Kirk