First thought I had was working on the negative space, since I really enjoy it and you've mentioned it in your brief. This being said I started thinking of ways to incorporate the G and the U, or the G and the upper arrow, in a way that would work in the negative space of the G, and could be directly related to "Geddup". I've also read that you were into art deco / futurism so I've made a google search and this poped up:
Very interesting. I hadn't seen the "u" - so the shape wasn't making sense. Now that I see the context (being the pictures) it makes a bigger impact. So the objective was good, but something got lost in translation. Maybe it needs more context to make it work - drawing on the whole word perhaps?
Unfortunately, I'm new in LT so my entries have to go through administration before appearing in your contest. That being said, I've uploaded 3 more entries that would be available soon to you, but I'll give you the info now.
The "stylized" ones, were created before you made that second comment. It's the same concept, with a different execution. You can now see which way you prefer me to work on.
The last entry, was made after I've read your comment and regarding the "drawing the whole word" aspect. I wanted you to see how it looked like.
All this being said, please provide any additional information you think would help me achieve the best possible solution for your project, and if I came up with any more ideas I'll post them.