At wide-open, the carbs run on the main jet. The only time I've seen a main jet clog was on a GS850 that sat for ten years with a broken petcock. The gas was like syrup.
On your Honda, and just about every other carb, the jet needle pulls out of the main jet as the diaphragm/piston rises. On my old GS1000, the throttle cable controls the rising brass piston. But after 1980, the plastic piston rises due to the vacuum of the engine.
That piston, and the walls that the piston rises in, has to be squeaky clean for the light vacuum to lift the piston out of the main jet. I don't know about your 600, but on my CBR1000, I can pull the airbox back and lift up each piston in the carb with my finger. There should be light resistance, and it should fall with a plastic thunk when released as there is a light spring under the piston. If all four don't do that, you will have to take them apart and clean them.
I don't know how mine get so dirty with varnish, as I have to clean them twice a year. But when they are clean, the throttle response is instant.
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