Given this was the OPs first game; i think everything he did was right on point and fine.
As he gains more experiences; maybe he can take larger risks.
That said; these machines are too damn expensive to take any risk really.
To the Distributor whom emails all his customers about what to do; good on him, but I'm not sure I agree with everything he says.

It's the responsibility of Stern to pack these well.
It's the responsibility of the shipping company to handle them with care and patience.
Anything else; falls outside the scope of this discussion.

The shipping company fuxed up. It's their responsibility to make it right. Not expect the distributor to look it over. Nor expect EITHER party to pay for services not rendered. It's on the shipping company to return a new product in new condition.

The shipping company needs to refund the original shipping charge. Period. As they did not render services expected or implied.
If the OP goes and picks up the game; then the above statement is def true. If they reship the good game "white glove" without additional damage and without additional charge; then they get to keep the original shipping charge.