I might have some insite on this, I did the three peaks challenge in June 2011. At the same time a team from the British army were indeed doing three peaks three times. They started at nevis the same time as us,midday, they were coming down as we were still going up. We arrived at the car park at scarfel the same time as them and had a chat. From memory it was 2 guys with a third that was doing all the support ie driving and cooking but not hiking, they would sleep during the drives and hot meals would be ready for them at the bottom of each hike, they were in a mini bus that I got the impression was slow or they kept to speed limits, they passed us on Snowden and commented that they are about to do Snowden again. So their route was nevis, scar, snow, snow, scar, nevis, nevis , scar, snow. Dont know if it was these guys but a coincidence if not.
Our group was successful, 4 of us, 22:45 from nevis car park to Snowden car park, we slept and ate on the drives , we didnt necessarily follow the speed limits but the we were tired driving in dark from nevis to scarfel and had traffic from scarfel to snowden, we shared the driving equally, we all started and finished together. None of us were seasoned hikers, weather was very good although we did see a bit of everything. Great experience