Not to be contrary or a devil's advocate, but everything said in the first post points to an ignition problem. The motor dying instantly, the dying when pulling in the clutch, and starts in first, but won't start when cruising all points to something (safety switches, ignition switch, coils, spark plug wires, etc) preventing a spark from getting to the plugs. And by the way, I personally know that Honda's spark generator can go bad and leave you with no spark advance, and possibly with no spark.
The rubber boots things and those white velocity stacks appear to be on the air filter side of the carbs. Any leaks on this side of the carbs won't affect air mixture, only letting in unfiltered air. Your picture of the air cleaner side of the carbs shows four air bleeds (those brass jets). Not familiar with your carbs, but one or more lets air into the idle mixture, one or more lets air into the choke mixture, and one or more lets air into the vacuum chamber on top of the carbs.
I think now is the time to take one of those black chambers off the top of one carb (watch out for the spring) and see how clean the piston and piston walls are. One reason it runs well at high rpm may be that the pistons/walls are so dirty the piston stays wide open (doesn't come back down), so the bike is always running on the fully open main jet.