I think the bit you're missing is that when you move in a particular direction, light from that direction becomes slightly bluer and light behind you becomes slightly red.

If you assume the "expanding balloon" is expanding everywhere at the same rate, by looking at the colour of the expanding balloon you can determine a speed relative to you where the balloon will have the same colour everywhere.

Yes, it would have been more logical if we'd have been stationary relative to the global frame, but it turns out we're not. Science is more interesting when it gives you answers you don't expect.

(It could be that the "bubble" is not expanding at a uniform rate everywhere, but we (currently) have no way of distinguishing that. And it seems the weaker assumption that we're simply moving than some fancy new physics.)