I've done my share of flashing ROMS, and I don't think it gets easier than this. I personally use too many of TW's features to do this, but here it is for those who want it.
http://m.technobuffalo.com/videos/how-to-turn-a-galaxy-s4-into-a-google-edition-phone/
Technically it doesn't turn it into a GE S4 as you can not receive and install OTA updates. Fundamentally its a just a 'port' of the GE with quite a lot of changes added (just look at the change log) - I should know I've flashed it enough in the last few days...
This is why it is in the android development section of XDA and not 'original android development' section.
Also as I've noted on the XDA forum thread itself, battery life really sucks on this latest version despite all the recommended fixes.
Also IMPORTANT the article uses TWRP recovery. This has led to lots of bad flashes with this rom. The recommended recovery is Philz Recovery for this rom if you want to avoid boot loops. Avoid TWRP for Jamal's 4.3 AOSP Rom.
Also if you flash Philz recovery via ODIN you do not need to root first.
But seriously folks - wait this one out for the moment until they sort out the battery drain on the current version...