Luckily, the second one did without any additional demands. As I knew to hail a taxi with a meter so I wouldn't be ripped off in negotiations, I expected the driver to request a bit more than the meter to help since he probably couldn't get a fare back into town. He didn't, so I offered him a little bit more anyway upon arrival, just to be nice.
When I arrived back at the hotel, I met my roommate for the first part of the tour, Nick (I had not paid a single supplement to guarantee my own room).
Thus concludes my first day of Egyptian adventure. We'd begin the tour itinerary proper the next morning.