That's a very good "rule of thumb" and applies to like 99% of the carbs out there. These 650s have a true "mixture" screw so turning it out makes the idle circuit richer. But it's only for fine tuning and only controls about 25% of the mix coming from the pilot jet. There are 4 tiny holes that let the air/fuel mix from the pilot jet into the main bore. Three are clustered together at the top of the main bore about where the butterfly plate closes and the fourth is off to the side. This fourth hole comes from the mix screw and you can "regulate" it's flow. On the other three, the only way to change the mix strength they put out is to change the pilot jet size .....
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When you clean these carbs, one of the things you check is that all 4 of these little holes are clear. I start with something mild like WD40, blowing it through from the pilot inlet on the bottom of the carb's main body. I only resort to carb cleaner if I find any of the holes plugged .....
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First I block off the mix screw hole on the outside of the carb and it's inlet into the bore, and blow the WD40 through. This tests the three little holes. Then I block them off along with the mix screw hole on the outside of the carb and blow more WD40 through. This tests the mix screw inlet. Then you can "back flush" the circuit by blowing WD40 in from the mix screw hole on the outside of the carb while blocking off all 4 of the little holes in the bore. It should come out the pilot inlet on the bottom of the carb body. You can alternate which holes the WD40 comes out by blocking all the others. For instance, block the pilot inlet and the mix screw outlet, and the WD40 will come out the three little holes.
You may need to revisit cleaning the pilot circuit because you shouldn't need 3 turns on your mix screws. It sounds like they're not flowing enough. On the several sets of '76-'77 carbs I've set up, they all only needed around the spec (1.5 turns out).
When I jet a set of carbs, I start on top with the mains because they influence all the other circuits and settings. I increase the mains one size at a time until I get stumbling in the upper midrange, in the midrange to main transition area. This happens eventually because of that circuit overlap I mentioned to you. Then I'll lean the needles a step to "fix" the upper midrange "stumbles". The stock pilot is usually fine until I lean the needles. Then a larger pilot may be needed because leaning the needle often creates a flat spot in the idle to midrange transition area. The larger pilot "fixes" that.
So, you seem to be going at this ass-backwards, lol, starting with the pilot jet and needle setting. What size mains are you running?