I don't know if this is helpful at all, but I packed a pin bound for NZ this year. The buyer made arrangements for it. Most of my USA pinball peers thought I was nuts for doing it, but the buyer really wanted the pin for its theme (CE3K). Now that I've done it, its not too bad and I'd be okay with doing it again, but unfortunately I don't have a FG.

The way the buyer arranged shipping was similar to the way you describe: put the game on a truck to deliver to a port, put the game in a container, have container make trip to Christchurch, NZ, and then pick up at dock or have delivered to residence/business. The buyer also paid for crating. The process was very long - nearly a month until the buyer received the game after it left my residence. Not sure how expensive it was for him, but I imagine it was probably 700USD or more. For a Family Guy, it makes sense.

Aside: If your'e ever in Oamaru, the buyer runs a pop-culture museum there (The Time Travelers Experience) with a large collection of items from American and British sci-fi: Star Trek, Dr. Who, and more. He built his own TARDIS, daleks, a time machine ala H.G. Wells, and more. TBH, that was part of the reason I considered working with him - he had a crazy vision for his museum that I just couldn't ignore, and everything else fell into place to get it shipped there. The CE3K is part of the collection, was converted to run on NZ currency, and is playable by patrons.