Okay, assuming you have 77 model carbs...
The book says that the pilot screws should be around 1 1/2 turns out from seated. These meter fuel not air. Turn in- lean, turn out- rich. You need a right angle screwdriver to adjust these properly on the bike. I made one for myself. But, elsewhere on this site is a discussion of where they can be purchased. Be careful not to ruin the needle or seat by tightening it up too much. 1 1/2 turns is starting point appropriate for a bike with stock exhaust and induction components.
The float height for these carbs is 14.5 mm. If you set them to 22mm like what the clymer manual says... well, that's wrong.
I'm not sure about the 77 carbs but the older model slides have a keyway. If you swapped the slides 3 and 4 into 1 and 2 carb bodies they would be backwards and won't close or work properly. The bottoms of the slides are angled, and the side that faces the air filter should open first.
Carb synch is described in the Honda CB550 Shop manual. Chapter 19 covers your carbs. Do you have 4 manometers? Or, are you planning to just mechanical sync them?
BTW, your carbs must be synced to number two as that one does not have a slide position adjustment.
Hard to say for sure with the current problem description. But, your carbs have four fuel metering devices, Main jet for WOT, slide tapered needles and jet for mid range throttle, idle or slow jets for low throttle position, and then the fine tune idle mixture screws and seats. Your current problem description does fit the slow jets or circuits being clogged. They are only .38mm (about .016 inch) in diameter, are pressed in, and they and pathways behind them are difficult to flush clear. If they are blocked, then the engine would only run when the carbs are operating on slide needles. And, without the addition of idle circuit flow, choke would be required for mixture offset.
But, I'm just guessing...