Could you please clarify the history of the carb? Was this new 3k miles ago or was it just overhauled and the jets and throttle slide renewed etc. Also, was everything ok with the bike's running over the last 3k miles and the problem has developed recently.
Assuming, it wasn't a new carb, the big problem with overhauling old carbs is that as well as the throttle slide wearing, the slide body against which it rubs also wears. If there's too much wear even with a new slide, air can leak past especially when you create max vacuum by snapping open the throttle!