I love the Giants colours, and I'm warming to the 'G', but I still think they should come up with a better logo at some point.
One of my favourite jumpers from the 80's, was the Woodville Warriors jumper, the yellow jumper with a green yoke with a 'Warrior' head on it, which looked to me kind of like a robot head, which I thought looked really cool, and I was thinking that a great interpretation of the name Giants, could be a giant robot character like one of those robots in Transformers, or something like that.
So instead of a slanted G, they could have a stylized robot head in the middle of their jumper, which I think would look unique and modern and would give them a bit more of an identity. They want to convert the next generation while they're young, and kids love robots.
As cool as this looks in my head, I don't have the graphic design skills to realize it, but maybe one of the talented designers here could have a crack, if they think it's worthwhile.