I think you'd have to go with less than seven, and leave Palestine out as a major power. Egypt, Saudi Arabia, Iran, Iraq, and Israel makes 5; if you insist on 7, the game could include Turkey and Syria. Perhaps choosing one one of those countries and making a six player variant could work too.
Starts could be
Egypt - A Cairo, F Aswan, A Alexandria
Saudi Arabia - A Riyadh, F Jeddah, A Buraidah
Iran - F Tehran, A Mashhad, A Isfahan
Iraq - A Baghdad, F Basra, A Mosul
Israel - A Jerusalem, A Tel Aviv, F Haifa
Turkey - A Ankara, A Istanbul, F Adana
Syria - A Damascus, A Aleppo, F Latakia
But yeah, that`s just a suggestion.