After the restart, all I need to do is move the Built-In Headphones slider slightly and the volume is reset to the level indicated by the Built-in slider. The startup chime will also use this setting.
The purpose of the two separate sliders is to provide the ability to control the sound output for the internal speaker versus the headphones. That is, you may wish to have the sound play very softly (or no sound at all) out of the internal speaker, but you may also want to have the the sound play loudly out of the headphones.
The workaround is to set both the Built-in and Built-in Headphones sliders to the same position. Later revisions of the Mac OS have only one volume slider.