Spend an extra night or two at Ras Sheitan. Then take the public bus south to Dahab and spend a couple of nights there.
From Dahab, take a bus or taxi north to the Taba international land border into Eilat Israel (EU citizens require no Israeli visa ). To reach Jordan, use a waiting Israeli taxi (on the meter) to the Yitzhak Rabin international land border. Pay the Israeli land exit tax, 103NIS or in US$ or credit card, and enter Jordan (no Jordanian visa is required at this border). Use a waiting taxi into Aqaba.
Leave Dahab Wednesday at 08:00 you will be having lunch in Aqaba the same day. The land border is considered cheaper, faster and more hygienic than the Nuweiba –Aqaba ferry.