Tour of the Roman Empire
My favourite bits of Jordan are Hammamat Ma'in, Petra and Wadi Rum, but very western and relatively expensive. In Syria, very friendly people, also the most arabic. Hama is a relaxed town.
I see a girl got a transit visa for Libya in Tunisia, but Cairo is a different matter, so I would try London. Good camp site at Ras Shitan, 20 K north of Nuweiba. Also if you want to ride from Baharia to Siwa you need to get permit in Cairo, the other way is OK (permit in Siwa)