I wonder if your fear is not because of the 2 engines and more because of the long flight. I used to only select 747 flights because of the long flight...I felt safer with the 4 engines. I would not fly a 777... That has gone away with time. I typically all classes (mostly economy and WT+) and an occational club world... Economy on a 777 is more confortable than on a 747. The 747 is a nicer flight, but there is nothing to worry. As many have say, the accident rates are not significant to get all out of shape.

A couple of years back, a lady sat next to me on a 777. When they closed the door, she went on a panic attack. We talked later and she said that is normal for her..... 30 minutes before arrival... there she went on... another panic attack. She would just cough with no end... but she said to me that was no reason for her not to fly.