A simple check of the float levels can be done on the bike, with the bike properly leveled on the centre stand, etc. Adjusting them is best done off the bike.
In the event a drain is plugged, the carbs have to come off, the bowl removed, and the drain cleared, so it's probably best to check them off the bike afterwards.
Having removed the carbs, make sure the drain screw will turn. You can gently clamp the rack in a wooden vice to hold things steady while you use a GOOD screwdriver to remove the screw. Heat may seem like a good idea until you realize the carb bowl is now full of gasoline vapour, so you'll have to rely on holding the screwdriver very straight, lean in real hard, and turn if it's stuck.
Once all the screws are free, remove the bowl(s) (being careful not to lose the little pin holding the float in place -- it's kept from sliding out by the bowl) and soak with some carb cleaner overnight. Remove the drain screw completely and try spraying into the bowl from the drain screw side. This is just about the only passage in the carb where it is permissible to poke with a piece of wire. Once the obstruction is cleared, spray it out thoroughly, or even soak it again. Replace the bowl when you are satisfied.
To check the float levels, you will need a piece of 1/4" clear plastic tube about a foot long, and another piece of 5/16" tube long enough to reach from your elevated fuel supply to the carb inlet. You will also need some means of holding the bank steady and level. I just use a B&D workmate, beside my workbench. The workmate is lower than my workbench, so I put the bike's gas tank on it, and gently clamp the carb bank across the mating faces of the carb air intakes and outlets. This leaves the bowls hanging free below the top of the workmate, so I can easily remove them during the adjustments. Putting a spirit level across the chrome diaphragm covers usually levels them nicely, but you can check with the tube, as shown in the manual. I also put a pan on the floor below the bank to catch any spilled fuel.
Connect the tank to the bank with the 5/16" tubing, and turn the petcock to PRI to fill the bowls. Connect the 1/4" tube to the bowl drain, lift the hose high to the side of the bank, and open the drain screw. When the hose fills with fuel, slowly lower it alongside the bowl edge, and measure the level. NEVER lift the hose up -- you will not get an accurate reading!
The float needle valve acts like a check valve -- it lets fuel into the bowl, but not back out. So, if you fill the clear plastic tube and lift it up to the side of the carb body, the excess fuel in the tube drains back into the bowl raising the fuel level artificially, making it appear that the fuel level is higher than it really is. Conversely, lowering the hose causes fuel to flow into the hose, lowering the fuel level in the bowl until the float valve opens. At this point, the fuel level in the tube will not drop further and reflects the real level of the float setting. You can now stop lowering the hose and take the reading. Watch carefully: while it is normal for the level to bounce back up slightly after lowering the hose, a steady rise in level that does not stop indicates a leaky needle valve that needs cleaning or replacement.
Shut the fuel off, drain and remove the bowl, and adjust the float as required. (TINY adjustments here -- a slight bend makes a big difference) Re-install and check. Yes, the +/- 1mm is important.
When you're happy, move on to the next carb, draining your 1/4" tube between each check to prevent an air lock and inaccurate readings.
One last final note:
I would give serious consideration to doing a complete cleaning of all the carbs while you have them off. You already have some kind of sediment problem plugging up the bowl drain. The odds are good that the carbs would benefit from a proper and complete cleaning