The hole in the line causes a loss of fuel pressure regardless of the fuel level in the tank which in turn causes poor running when this happens.
The short cycle of the pump you mention could be because there was residual pressure still in the system from the first start seconds before.
The first post you mentioned that the cap off made a difference, that's why I thought a bad vent in the cap.
Your problem sounds as if it could be a crank sensor going bad or possibly another sensor.You may have to check the sensor out to see if it is loosing the signal with a meter.
Crank Sensor (CKP) - Harley Davidson Community
Have you checked for codes and is the light lit in the speedo?