Unfortunately I've had lots of experience with stuck, gummed up carburetors. Safest way to fix them is to soak them a day or 2 in fuel or rubbing alcohol. I like that guy's idea of boiling the carb but I've never done it. I have used a propane torch but that is dangerous. Will melt hidden plastic or rubber parts and ruin the carb. I have tried a big electric soldering iron, but it didn't work for me.
You said one carb was broken. That the arm moves but not the barrel. Very common. You can't tighten the arm tight enough to turn a stuck barrel, especially a plastic arm. So the carb isn't broken, just a stuck barrel.
Good luck!