After such a long period of sitting, O-rings may have shrunk and as a consequence will leak. Usually after a wile of being in contact with fuel again, they can swell back to their original size and seal again. I have seen this happen more than once, especially those around the T-joints, where the fuel is distributed. It saves you separating the carbs from the rack.
All in all it may well be, you got to have the rack on the table. I just read you have it already there.
This would be my working order. Open floatbowls and remove the jets, tubes, etc for inspection. Have 4 bowls ready 'cause you want to keep parts of each carb separated. Clean and refit.
The little O-rings around the main jets may need to be renewed. You can pull the needle jets, once you have removed the main jets. This is best done by bringing the slides in full throttle position and insert a wooden pick from below, cant it and usually you can wiggle the tubes out. Anyway, I always managed without having to open the carb top lids. WD-40 or similar stuff may help. Slow jets in particular need to be cleaned and now you're at it, you may as well spray some carbcleaner in all four orifices of each slow circuit. Apart from the slow jet itself, these orifices normally stay clean, but now you're at it, it won't harm checking the passages are clear. When you remove the airscrews from the sides, first make notes of how many turns out they're set now. You do this by counting the turns when you screw them in completely, but gently! Realise they may have been set in various positions by Honda or dealer. So make notes.
Carefully remove the floats, floatpins and floatneedles and inspect them using a magnifying glass. Especially the floatpins, the tip of the floatneedles and the corresponding valve seats probably will need cleaning and some light polishing without using abbrasive stuff however.
Do NOT 'adjust' the floattangs unless you are 100% convinced they have been messed with by a PO.
Normally they don't need readjusting ever.
All the brassware can be reused. I'd abstain from ultrasonic cleaning. May work for other carbs. Yours don't need it.
After refitting the parts and closing the bowls, I would bring the rack in a test position and add fuel through the fuelline(s) and... wait. Even when the supply route leaks somewhere, give it time! As said, it may swell up again to its original size.