Time for someone to disassemble and clean the carb. Sounds like the issue is in the main jet passage. These bikes do not come standard with an accelerator pump and as a result can be a little picky when it comes to WOT just off idle. Also, with reduced back pressure in the exhaust from the leaking at the broken stud, you are adding to the issue. Clean the carb (pull it all apart and soak it in Berrymans or like solution), replace the internal O-rings, fix the exhaust stud, and you'll be golden. Also... when was the last time you set the valves? Good Luck.
The Goal... All I Need Is The Time...