You're very welcome.
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:
http://i.imgur.com/rebUZ.jpg(I've circuled the ones I used as reference)
So I started looking for a way to do a futuristic G with "squared'ish" lines, and incorporated a "U" inside in a natural almost instinctive way.
The font is also pretty similar to the symbol, and futuristic itself.
Now as for your question: what to you mean by a "stylised" g? Can I see some examples?
Thank you,
Tiago