AHBA, BADR or air taxi are good bets, AZZA operates a 707 here as did Sudan Air for a while so they will have the equipment you need. Failing that, contact Saudi air (they fly a 74 here daily) or MK airlines, they had a 6 month gig here, not sure who did the handeling but I am sure they could tell you. If not PM me the full details and I will make some calls.
Dog