Have you checked your options with Turkish Airlines through Houston? We are flying on Turkish Airlines in April/May from Houston to Hurghada via Istanbul. At the time I booked it was less than $1,000 per person
Dammit, we're on the same flight at end of May for $1200. Some of the flights were $1500. We have a long layover in Ataturk and a 3am arrival in Hurghada. There is an earlier Istanbul to Hurghada flight that reduces the layover and gets you in around 10:30pm but only on 3 days per week.