You have the most current bystarter and bowl.
Before you take the carbs back apart....
Did you vacuum balance the carburetors? That is important to do to these Hondas. When you do, you will need to clamp off the vertical hoses running between the outside of #1 to #2 and #2 to #3. You also have to clamp off the smaller hose running accross the top of the #1 (top) carburetor.
Once you clamp them off while the motor is running, you will probably have to readjust the idle stop to get it to idle 950 plus/minus 50. I like to set it on the higher side. Make sure that you make the adjustment with the engine warm (but after 30 years, you probably know that).
Once you balance it and remove the clamps, the idle will go up....so you will have to readjust.
When you try to restart, be sure that the fuel bulb is hard and the throttle is all the way down.
If that does not improve it, then go back to the top carburetor and pay close attention to the bowl and all its passages. The extra fuel for starting is picked up by the narrow tube going up to the bystarter. Make sure the tube is clean and when you fill up the bowl with solvent, the hole in the bowl where the tube goes into should have fuel in it. If not....more cleaning is involved or sometimes just get a new bowl.
Mike