Post-trip update:

I went on the tour with my family on August 15. We ended up with a 23.5 hour layover, arriving at 9 PM Aug 14 and leaving 8:30 PM Aug 15. We checked all of our bags through, which turned out to be the right choice, by far.

We self-booked a cheap hotel near the airport for Sunday evening. At ~$68 for the whole family, it was far cheaper to book a hotel and get the free tour than get a hotel and pay for a tour.

We had no trouble getting in to the airport on Monday morning and qualifying for the tour. The tour itself filled two coach buses. We were dropped off for breakfast near the Old City, and the rest of the day was a walking tour from that point. Half the group went back on one bus after lunch, and the rest of us spent the afternoon in the market before going back to the airport.

If we hadn't checked our bags through, they would have stayed on the bus and been moved around by local staff since the bus taking us back to the airport wasn't the same one we came on. It was nice not to have to deal with that. Luckily, it all magically appeared on the belt at our final destination, a day and a half after we left Paris

One thing to note. The roads leading into the airport were very crowded due to the security situation, as was the security line itself at the airport. They seemed to cut the tour a bit from the itinerary on line to get us back a bit earlier. We saw most of what was on the itinerary, but there was at least on attraction that we walked past without going in, and no comment from the guide.

Overall though, great tour if you have or can work out a layover that works with their schedules.