I forget which walkway is the fastest. But I'm sure somebody else knows.
Your best bet is to get to EE first thing and grab your FPs. If the line isn't long, then you can wait in line and ride it then. Then go off and do some of the other rides, then come back during your time and you can ride it again with your FP.
Since EE is a new and very popular ride, the lines can get pretty long, even on off seasons. During the busy seasons, I'm sure its probably a 2 hour wait the whole day. So definitely go grab FP's as soon as you get into the park.
Have fun! EE is such an incredible ride!!