I would not attempt shipping around this time -- too many delays and it's simply too cold. If have to ship, airport to airport is best. Otherwise, I suggest having your LFS order one for you. That way it'll most likely come with a pooled order, in a larger styrofoam box with better attention to packing.
For the next attempt, I would go with a larger QT system. 10 gallons is about right. I think gigantea react to osmotic pressure (they can sense how much water is around them) and in my experience a 10 gallon tank worked a lot better than one that was filled with only 5 gallons. You really want to dilute the pathogen and waste to the point where it isn't drastically affecting the gig.
Lastly, if the gig doesn't inflate, it's not taking in much medication. Looked like yours never really had a fighting chance. Sorry.