I would guess either a carburetor synchronization issue, lean mixture screw(s), or there is still some varnish in the idle circuit of one or more carburetor. When you mash the throttle on your engine there is a rudimentary type of accelerator pump/dashpot that burps fuel out of the main metering tube by pushing air into the float bowl. If you accelerate slowly this does not happen and you may be leaning out as you open the throttle plates. There isn't enough fuel to keep up with the air.
It is almost impossible to clean the idle lift tubes without a ultrasonic cleaner like you would use with jewelry. Often times it is just easier to replace the tubes as you eliminate the possibility of missing a thin film of varnish that breaks loose later thus you are doing the job a second time.
Good luck,
Randy