Sounds like more than 1 problem, the 'stumble from idle' is from overexposed transition slot. This is common when the engine isn't quite running right and the idle speed is increased to compensate. When the idle speed is increased the throttleblade angle increased and that overexposes the transfer slot, the transfer slot is in the main body adjacent to the idle discharge hole, it is a thin slot extending up from the throttle blades. When the idle is proper the slot exposure will be about square below the throttleblade. The function of the slot is to provide fuel as the throttle blade sweeps open (called 'tip in') the slot see vacuum and reacts in milliseconds providing additional fuel to the engine until the squirter shot kicks in.
When the slot is overexposed the motor will stumble then the accelerator pump covers it up.
If you have big cam and need high idle you can open the secondary throttleblades a little and then close the primary blades down a little to keep the higher RPM without over exposing the transfer slot. There is a little screw in front of the secondary pumpshot plate that is accessed by turning the carb over, the screw is down in that hole.