There's really two things here, not one, the immediate application for immediate effects and the systematic application for systemic effects.
For getting you to sleep that night, yes, the 4 - 7 pm time frame is ideal for the start of the session. Fast for a few hours before you start drinking the kava, to increase the effects. Drink shells of good strong kava paced out 20 - 45 minutes apart, depending on how you feel, and plan to stop drinking kava at least 1 hour before bedtime, although really, 2 or 3 hours before bed for the last shell is ideal. Calm sounds, quiet music, low lighting, comfy couch, these all help set the mood of the sesh. In terms of quantity, somewhere between 3 and 12 TBS of medium grind, depending on how much you need and how much you enjoy. Most likely it will be in the 4 - 8 TBS range, though.