Most likely cause of what your experiencing is a blocked fuel supply that lets it run til the carb bowl is empty then it slowly refills again. When you flush the tank take apart the petcock and clean it out good, also put an inline fuel filter on it, that will help as well!
With the cost of the carbs being about the same as the rebuild kits i usually replace rather then repair unless the carb is in good shape, if its grungy inside or the slide is loose from wear i just junk them.
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....