Having just recently sorted out a similarly presenting problem bike, let me pose a few questions:
Have you ridden it any to determine how it runs when it gets out of the idle circuit? If so, how's it run?
The carb bowl covers can be removed with the carbs still on the bike. Just need a 7mm open end wrench. The right side front screw can be a little problematic with the throttle cable crowding your wrench space, but it works.
With the bowl covers off, it's easier to remove the main jet by removing the needle jet with an 8mm socket on a 1/4 drive ratchet. Separate as you see fit, but make sure all the little holes in the needle jet are clean & clear.
Next, is where it gets tricky. I will testify that it is in fact "possible" to remove the pilot jets with the carbs still on the bike, but it's a bear and you absolutely must have the right tools.
I used a Milwaukee Offset Screwdriver (tried to post a URL, but got shut down - Google it...)
The orifice in the pilot jets is TINY. I went through three different sizes of twist-tie wires, and two sizes of copper strands from braided wires before I got the clog cleared on my problem pilot jet. Wires are NOT recommended for cleaning jets & I know that, but that's how frustrated I was at the time. A good soak in carb cleaner and a shot or few of compressed air is a far better option.
The offset screwdriver is a royal PITA to get lined up, but it worked and was less painful that pulling the carbs, just make sure you get the main jet out of the way first so you can pretend to see what you're doing.
In any case, a case of beer says it's your pilot jets, and another case of beer says that a week's worth of Seafoam won't even make a dent in your problem.
On the bright side - it's totally fixable. So smile, you're halfway home (knowing is half the battle...