You're just lucky it's raining cats and dogs here, giving me time to exercise my english. Every now and then I'm distracted however by
another country that's fighting the effects of mass poisoning by Murdoch and the likes.
You can leave the airscrews where they are. I hope you have removed the main jets and have already squirted some WD-40 in the orifices where they sat. We can now remove the needle jets (aka emulsion tubes). You can see the pointed tips of the needles in there. It's not the needles that we are after, it's the tubes in which they slide up and down (see pic for an example). Turn the big central idle adjuster knob (well it's on the right actually, but by 'central' I mean it controls all 4 carbs) so that the gasslides rise. It is like giving more throttle. As a matter of fact you have to 'give even more throttle' by hand. This can be a bit hard, because the central return spring is a tough guy and hard to fight. We want the slides up but the
real goal is to raise the tapered needles inside the needle jets. Hopefully these needle jets just drop out by gravity. If not, gently tapping the carbs - the slides (and needles) are still up - can help. If they are still stuck, bring a wooden toothpick or similar in them from below, cant it and wiggle them out. This has always worked for me. The WD-40 you have squirted in there before, may help. The needle jets normally do not need maintenance. You may run a pipe cleaner through it, but nothing abbrasive. In the sides of the needle jets there's a serie of tiny holes. They are there to
help aerate the fuel. You may find some of them blocked with white stuff, the residu of water. You can use a pin to remove that residu without reaming the holes. You may squirt some carbcleaner towards the needles that will stay where they are.
Now to the main jets. Important is that their tiny O-rings are OK and will seal well. When in doubt, replace.
What else can we do? You could verify all vent tubes are open by blowing some air through them. You could check all chokeflaps move as they should, by playing the lever on the left.
Usually the O-rings around the valves (where fuel enters the carbs) are OK as they fit really tight. You
could remove them, but I personally have yet to see the first one that leaks. When you do, take note of how the retaining clip under the crosshead is orientated. Whether you remove the valves or not, is your choice, but
do blow air in the direction where the fuel comes from. The ^ shaped orifice in the valve (seen from the bottom), where the ^ tip of the floatneedle fits, can be cleaned with some WD-40 on a Q-tip. Do the same with the ^ tip of the floatneedle.
Assembly time. Put in the needle jets. No need to force them in. The main jets that follow, will do that for you. Just make sure the main jets go in with the tapered orifice up, this to accomodate the tapered needle tips above them. The main jets in their turn will be pressed by the leaf spring, but that comes later. After a final inspection fit the slow jets.
To ensure the floats will be moving up and down smoothly, it's not a bad idea to polish their swivel pins. Don't be tempted to 'adjust' the floattangs. We do not have ANY indication they need adjustment! You know ofcourse
how to position the float needles.
Check the floats can move up and down smoothly. To check float heights are correct, go to p. 60 of the Shop Manual Honda CB500 - CB550*. You don't need the float measuring tool shown there in fig. 183. Just cut your own out in an used card (see pic). Follow the instructions on p. 60 of the manual. Now,
if you think,
if, they need adjustment, think again. I never had to adjust them, not even one. Prescribed is 22mm. Don't worry about a mm more or less, it's acceptable and I'd rather have you keep your hands of them, to be honest. After you've put the springleafs on the main jets, you can put the floatbowls in place. You will feel some resistance which is OK. It tells you the springleaves are pressing the main jets in. I myself have replaced the 16 crossheads by allen screws (see pic). Believe it or not, ever since I can do practically all of what we have described sofar, with the carbs remaining in situ. I do
not recommend to do like I do the
first time, but once you know where things are, you can do it blindfolded.
The oldstyle CB500/550 Keihin carbs like to have the fuellines in the correct size. In your case it's a 30 cm long fuelline going to the T-joint that distributes fuel to carb 3 and 4 and one that is 18 cm long to the T-joint that distributes fuel to carb 1 and 2. Ideal internal ⌀ is 5,5 mm. Outside ⌀ will be around 10 mm. Abstain from inline fuel filters. They'll cause irregularities on a CB500/550.
I advise to add some fuel system cleaner to the fuel when you're ready to start riding. We here have Forté or Tunap, the Brits have Redex and I believe you have Seafoam. It's good stuff to clean and 'lube' (well not really, but kind of) parts like the swivel pins, and valve needle tips and valve orifices. Owners of K3 models IMO better have it added
always, unless they ride daily.
*
https://www.classiccycles.org/media//DIR_1653304/DIR_1653404/DIR_1653507/ecc6759db0a214d5ffff881effffe41e.pdf 
