OK my 2 cents, are these TWO carbs, OEM honda carb,s or china knock off off ebay or like places? which tend to be very HIT or miss, many good many more bad one's
as right there could be the issue
not all parts are made the same
but sounds to me like a float issue here as well
and if your not using fuel fast as a tank is lasting more than 2 months, and your NOT treating it(and should still be) or if your NOT running non ethanol fuel, the fuel itself can be the problem your carbs are not staying good
next will be, have you EVER removed the tank, drained and looked inside the tank, and MADE sure the tanks are clean inside
as you can clean a CARB< all you want, but if the tank is dirty, as soon s you run fuel into carb, you risk a dirty carb again
and last, just like a tank can get dirty inside, so can all things down stream, the peacock can get that same crappy ethanol build up on it, the fuel lines on MOST older atv's were NEVER designed to run ethanol fuel, and the fuel lines can also block up build up crap and it can break off at random and mess with your carb working right!
SO< my suggestion, drain tank, inspect inside to MAKE sure is clean, inspect peacock, and REPLACE fuel lines from tank to carb with NEW YELLOW tygon fuel line, its the only fuel line I know of that is MADE to handle Ethanol fuel!
re clean carb's and I BET your issue's go away, well unless there china junk carbs that are just bad as is!, but either way, problem solving is about ruling out possible things, and if your fuel take, peacock and fuel lines are all clean, well, all that is left is a BAD carb!