I've torn apart two of the four carbs (3&4, which feed the cylinders that seem to have the more pronounced carbon fouling) and in both cases there were nasty bits in the bowls but all the main and slow jets were clear. But you say that would cause too lean rather than too rich a mixture.
Yes, but that would explain erratic driveability When the engine is suckin on the carb, the carb draws fuel through the jets. Bounce. A nasty bit gets up to the jet but can't get though. Engine dies from fuel starvation (blocked jet), sucking stops, nasty bit falls back to bottom. Engine restart, fuel flow returns. rider says "What the F*^K?" Sound familiar?
HOWEVER, both floats were set too high (just resting on the valve pin without compressing the spring the height was 25mm, not the 22mm stated by the manuals). But too high a setting translates into a lower fuel level in the bowl, right, so how would that create a too rich situation?
Doesn't seem like it would to me either.
Also, the idle mixture air screw settings are all over the place and the manuals don't seem to agree on this one (Clymer says 1.5 to 2 turns out, versus Honda which says 1 plus or minus 1/8) turn. So, the further out, the leaner or richer the idle mix?
I have K&N pod-type filters which I cleaned and oiled when I pulled the bike out of storage.
These screws can make your idle mixture rich or lean. Turn them out to make it leaner and in to make it richer. The Honda spec assumes use of the stock filter with its restrictive characteristics. It also assumes the stock exhaust, too. Changes to these mean you will have find the correct idle mixture setting for your set up. They should all be set to the same number of turns. I would start with the factory setting.
Assuming everything else on the bike is happily working properly. I set these according to the throttle response desired. If they are too far out (Lean) the engine will tend to wheeze and die when applying throttle. If they are set to far in, the plugs can get sooty during idle periods. I turn them out a little at a time until I can't stand the throttle hesitation. Then back in just until I get the responsiveness I need from the throttle. This assumes the main jet and slide needles are already matched to the engine breathing requirements for the throttle settings they are in play.
I should probably give you two warnings here. One, it is possible to over-oil the foam in the filters. This can cause added restriction and will only effect the carbs that have the over-oiled pods. The added restriction will act as partial choke and make the mixture richer. You'll have to assess whether this condition applies to your situation.
And two, tuning and adjusting carbs is the last thing to do after a complete tuneup. The timing, plugs, cam chain tension, tappets, and air filter should all be in optimum condition before carbs are synchronized and fine tuned. Otherwise there is risk that you'll have to fine tune the carbs again after other changes are made. The good news is that once the carbs are fine tuned to the engine in this way. Future tune ups won't involve the carbs at all!
And as an aside, is there any reason not to use a little touch of anti-seize on external carb body screws?
I've never tried it. But, I know of no detrimental effects.
Also, since you are now into the carbs, check that the vent and drain hoses are clear. Insects can make nests in them, plugging them up. It's a simple check and a possible source path for nasty bits to enter the carb bowls.
Good Luck!