Rebuilding petcock is good start. Sounds like vacuum diaphragm is not working properly to stay open and let fuel flow. Also check main jet, very common for people to go up in jet size rather than clean/floss the hidden fuel passasges in their carbs. Please review this thread and linked threads within on proper carb-cleaning procedure.
https://www.ninjette.org/forums/showthread.php?t=323737