Doc,
What time is your connecting flight? Even though there is no precheck line at the Midfield, I would go through Midfield during that time period. The lines in the morning at IAD could be completely backed up at that time. I am not sure if South African lets transfer passengers do midfield so you could be one of the only 3 flights in midfield( GRU, KWI and DXB). Prob half or even more will go to Main Term due to DC being their last destination. Since you won't have any checked luggage, I would say it would maybe 15-20 minutes from entering customs/ immigrations to being at C7( where you enter from leaving the area). Walk to C14, take train 3 spots to the B concourse and then enter the British Lounge.