I imposed on myself an extra restriction that wasn't mentioned, so that frees up my thoughts a bit.
AGS-ATL, DL, 72S
ATL-BOS, DL, 72S
BOS-PWM, QO, CNA
PWM-AUG, QO, CNA
AUG-BOS, AN, DHT [AN = Air New England]
BOS-ATL, EA, 72S
ATL-AGS, DL, 73S
Let's see if that covers everything.
Northbound: 4 segments (check), 2 airlines (check), 3 aircraft (check)
Southbound: 3 segments (check), 3 airlines (check) - 1 repeat (check), 3 aircraft (check) - 1 repeat (check)