Unless there's a lot over overlap, isn't there in excess of 20 hours of time accounted for in the plan? There should be a noticable price difference between a 12-hour and 20-hour engagement.
I concur with those up thread, just ask him about his overnight rate. Don't ask for a discount with the number he gives you. And be prepared to pay for all incidentals during the date.
Absolutely this. Don't schedule an overnight if it's your first time meeting. If the vibe doesn't work, then you will still be out the money and you won't be satisfied.