It's kind of a Catch 22.
If STI wants to see the game before they take and wrap it, then you won't have time to pack it securely. STI looks it over for 1 second, puts moving blankets over the game, then wraps it in stretch wrap. That's their "professional packing".
You can do a MUCH better job packing yourself, but then STI might argue that they never saw the condition of the game - so take lots of pictures!
I leave it up to the client if they want STI looking at the game and STI wrapping it, or better packing with me wrapping it.
If there is anyplace likely to get damaged, it the corners of the game.
I steal these heavy duty fiberboard corner protectors from work, and run them along all the edges of the game:
I like these to go on top of the L protectors for the 8 corners of the backbox:
Plastic banding is good to keep all the L protectors in place before you stretch wrap. It comes in a kit with a tensioning tool and locking clips:
Put the clips on the bottom, so if the game gets banged around, the clips won't imprint themselves into the visible parts of the cab.