I think your biggest obstacle, may just be the beurocracy of getting the Saudi Transit visa to cross the country. As far as Jordan and Syria, Visas shouldn't be a problem for either, and don't worry, they are both very safe countrys. Once into Turkey after leaving Syria, you'll have no problems there as the only worries there are in the East of the country, and where you enter Turkey is well West of those areas. I would love to do it one day, and am very envious. I would say, however many hoops you have to jump through to get the required visas, you should do it, cos it will be an experience not a lot of people get to do. Good luck.
P.S If you do it don't miss, 1. Petra 2.Palmyra in Syria, 3. This local sweet cheese roll specialty from Alleppo (in Syria near border with Turkey). 4. Banana milkshake in centre of Damascus and 5. Food in Antalya (on Mediterannean coast of Turkey). Enjoy!