It can be done. Cairo, Luxor in the 2 days. The only caveat is that the plane lands in Cairo at 3:00 p.m. and "all aboard is at 7:15 p.m" and it is a 3:00 drive from Cairo to Alexandria. That leaves 1 hour 15 minutes for delay in plane or traffic.That is too close. However, we are scheduled on a flight next year from Luxor to Cairo and I believe that the plane is scheduled to land at 2:10PM. This is with Egypt Air.
Note there are also earlier flights back to Cairo. Why don't you fly back the next morning on the earlier flight?. Go to the Egypt Air website as there are more options.
I also thought they had or were planning flights directly from Alexandria.