Howdy Timbo!
Rebuilding the petcock is a fairly easy procedure once the tank is removed. It's four screws.
The number six vacuum line (left side rear) operates the system. If that vacuum line is bad, then the valve would stay off and the bike would not run.
But...if the cover set is bad, then the system would leak fuel enough to start, then not open enough while running which would starve the engine at higher RPM's.
If it were me, I'd do the simplest thing first...replace the cover set (re-build the petcock), replace the vacuum lines, then see how she reacts.
As old as these bikes are getting, a good carb cleaning is probably in your future. It's not as hard as you think!
Good luck! 