1. Yes, that butterfly clip looks correct. A bit of horizontal play in the needle is normal. There should not be any vertical play in the needle. The "wings" of the butterfly should clip into a grove at the base of the inside of the slip. You can gently bend them to have better tension of the butterfly "wings" if needed.
2. I use an ultrasonic cleaner after removing all parts from the carb bodies. I then clear it out with compressed air to confirm that they are not blocked.
Being one of the few lunatics who actually prefer the earlier carbs, I have a few thoughts...
1. As stated by Galactia and M750K6, check your float level and the condition of your needles. I too had high-quality aftermarket needles that were too thin and caused issues. Always best to go with original Honda part when you can.
2. Check the condition of your slides. Specifically, the diagonal part that the idle screw adjusts against. They can, over time, get grooves that give them weird behaviors (the side might not settle in the same place each time the engine goes to idle.
3. What is your manometer telling you? Remember that the early carbs allow you to set them at both idle and at speed. In other words, confirm that your carbs are synced at idle AND at ~3k RPM and watch them in between. Uneven readings can be a useful clue.
4. Confirm that your idle mixture screws are in good shape and set to factory spec.
Let us know what you find!
