This is my own special route I discovered! First, I use the button save glitch to not need the cube. Then, I shoot a portal through the opening in the E-field.
After arriving on the upper catwalk, I use a glitch (unfortunately, the person who discovered it has had his video removed, so I don't know who to give credit to) that allows you to go Out of Bounds in Portal 2. This has been the first use of that glitch in a speedrun route. Basically, you crouch inbetween portals, and load/save over and over, and you'll continue to go into the floor. I only needed 2 saves to get into the room below the catwalk.
I continue to use the button save glitch twice more to get to the elevator's catwalk and exit the level. Enjoy!