If it's leaking petrol, I would be looking for the leak and following the petrol route, tank to filter, filter to pump, pump to carbs. And then look under the carbs to see which one was the problem.
That does seem strange to me that opening the fuel tap causes the engine to bog down?!
I also can't help noticing that your carbs are odd to. The left bowls and different to the right?! I'm pretty sure mine isn't like that.
With running issues you can usually determine which cylinder/carb is at fault by the exhaust temperatures. The highly accurate spit on finger sizzle test is a good indicator.
IMHO, people are always a bit hasty to get the carbs off and in bits, which despite being a ball ache is rarely the issue.
I hope you get it sorted.
