Air filter is new and installed last fall. Still looks good.
I've found I can't tell a clear filter from a restricted one by simply looking at it. Honda recommends the paper filter be cleaned at 3000mi./6 mo intervals and replaced at 6000mi./12 month intervals. When I stretched the paper air filter use in my 550, the plugs got sooty much faster. I eventually switched to the Uni Nu-4055, simply because of the economics.
As a test, clean or replace the plugs, remove the filter temporarily to see if the problem persists, or improves.
Emulsion tubes cleaned when carbs were rebuilt.
Vacuum synch completed this winter.
I think I asked this before, but is the current malady a recent development, or a continuation of problems since the last tune-up/carb rebuild, or maintenance cycle.
I'll just say that since the bike generally runs but has a small annoying condition, it is likely the bike's issue is in some smaller detail.
Not simply trying to be a stickler, but I asked if both emulsion tubes in each carb were cleaned. Your response made it unclear if all eight were cleaned, which may or may not be what your assumption of "all" included.
You say vacuum sync performed last winter. Not relayed, is if the current annoyance was present last winter or developed recently, possibly with a slippage of the vacuum synch adjustment.
Personally, I find that when the engine behaves badly the first thing I do is is address (check or adjust)
ALL the 3K tune up items. Usually, this corrects bad behavior. But if it doesn't, I know it is not a routine correction but, something certain out of whack elsewhere.
One method of troubleshooting, is to isolate items from the "unknown" to the "known good" category. The assumption is that if all components of the system are in the "known good" category, you have a properly functioning machine.
If your check list tallies all items as "known good" components and your machine DOESN'T behave as it should. There was a mistake in claiming one of the components as "known good".
Personally, I don't want to dismantle carbs, only to find out one of the 3K tune up items was amiss, or the vacuum sync adjusters had drifted.
Anyway I can only advise, you have to do the work.