You say the oiil pressure switch is OK!
Does the unit have oil pressure!
Needs both oil pressure and 120vAC to stay running when the start switch is released!
Do not hold down the run switch to keep it running until you confirm you do have oil pressure! I do not remember if the oil pressure switch is open or closed at rest with zero oil pressure! The switch will switch states from open to closed or vice versa if it has oil pressure when starting or fast cranking!