I agree that you should just walk around instead of cutting through the parking lots, though I think it's worth it to follow the people mover signs to the third floor and take advantage of the moving walkways.

If you want to go to the FL from outside security and you are coming from the other side of the airport, your best choice is not the E-Terminal security, but the tiny, hidden checkpoint that is just a little bit past that as you are coming back from GE. It's the one they used while they were renovating the E-Terminal security area. It dumps you out into Terminal D right where the walkway from Terminal E enters Terminal D by gate D-31. On each of my last two trips, I had to leave the FL and go somewhere outside security and then return to the FL. This security location worked perfectly for that both times. This past Saturday, there were zero people in line when I re-entered. Of course there is no Pre-Check, but the only difference is that you need to pull your computers and tablets out of your bag.

If you are leaving from the FL, follow the signs to Terminal E. Right after you pass gate D-31, instead of turning right into the corridor to Terminal E, just keep going straight.

As you are returning from GE, walk until you see a Taco Bell on your left, then turn left to get to this security area. If you get to the big wall of glass where international arriving passengers are leaving customs, you have gone too far - it's right before that.

Warning - I am not sure that this entrance is always open, since it is so small, but it has been every time that I've tried to use it. If you are leaving from the FL, then try to go out than entrance to see if it's open, and if not, continue down the corridor to the regular E-Terminal security. That's your second-best choice for an exit and return to the FL if you are coming from the other end of the airport IMHO.

NOTE: This is also my entrance of choice when the security lines in international arrivals are crazy. As you leave the int'l arrivals area on the first floor, turn right, go up the escalators and you will see the Taco Bell.