That rusty tank is going to cause you trouble until you seal it, replace it, or try some other trusted cure. That super fine rust is great at sifting through filters then binding together while it sits in the carb's float bowl.
Pull off that air cleaner and take a look down the throat of the carb. Is the slide moving all the way up? Is the needle coming up with it? Normally dirty carbs have lots of trouble on the low throttle openings and rev just fine. Your sluething with running it out of fuel would lead back to the fuel system, though not necessarily to a plugged jets. Still, if you do take another apart, make sure to take it completely apart, including the enricher circuit / choke. The main jet and the needle jet that it screws into need to come out, as does anything else that has any sort of passage.
Sorry I can't help you with the broken pilot jet. Buy a new jet, buy a matching tap, and go to town for one last great try would be my approach. I hope somebody else has a better idea for you. Else, look up
http://www.bikeboneyard.com and Brendan will probably have a carb for you. I do have one for the CR250M, but I don't know if that might be just different enough to require more fiddling and I sure don't expect you have the patience for that right now. Good luck! Jon