The slide cutaways face the carb inlet/air filter. You should be keeping each slide with its mated bore in the carb.
The hole in the slide you are fretting about, is done by the factory. The hole's purpose is to prevent a vacuum lock impeding the slide movement when the top covers are on and sealed. I've never noticed that vacuum balance is effected with top covers on or off.
These carbs worked fine from the factory. Imo, you should be focusing on things that are different from factory configuration, like dirt, corrosion, or tampering.
The bowl vent/pressure equalizer openings allow atmospheric pressure into the top of the fuel in the bowls. It is this pressure that pushes the fuel through the metering jets when the cylinder makes lower pressure in the carb throat. The "vent" system is coupled to all the carb bowls at the top of the bowl cavity. However, each of the bowl overflow stand pipes also allow atmo pressure into the bowl cavity, as long as they aren't blocked by overflowing liquid. Therefore, plugging the top bowl vent tube won't effect your current run problem, provided any of the 4 bowl drain tubes are clear.
That is not to say the top "vent" tube should be plugged. It should be open and have a tube long enough to discourage dust, dirt and insects from making its way into the carb bowl cavities. Originally that tube ran back and down to a point between swing arm pivot and back of engine case.
At some point, you should review and correct the air plenum drain hose, and the air filter box drain hoses, as capping them off disables their true purpose. However, defeating these, will not cause "hanging idle".