TL;DR: Amazon US BOTW Special Edition said "March 14th," a quick email made them correct it to March 3rd within 4 hours.
Back story: I stayed up and pre-ordered my Switch at 3 AM EST and was lucky enough to nab a BOTW Special Edition in the morning, all from Amazon US.
Today: My BOTW Special Edition still said "Arriving March 14." I was a bit worried and read on this sub that others had similar issues. I decided to email Amazon, saying:
"All versions of this game release on March 3rd according to Nintendo. Is this estimated delivery just inaccurate, or am I really going to receive it 11 days late? I would be quite upset to have to wait 11 days to play a game that releases on the 3rd and will be my only game for the Nintendo Switch, which also releases on the 3rd. "
I received a response almost immediately (yay Prime):
"Please allow me to explain in this case, When the per-orders are placed, the orders are shipped on "First come First served basis". In this case I see that order was placed on Friday, January 13, 2017 11:58 AM (PST), however your item being a pre-ordered product and is placed by our customers on demand.
However to help you with this, I tried to upgrade the shipment, but as there were no option, I was unable to do so. I hope you understand my limitation in this regard.
Further, I've also escalated the issue to our fulfillment center, so that if any changes can be made and it can be upgraded."
Now: Four hours later, I received an email telling me order has been updated with a new release date, arriving March 3rd!! I'm very relieved I won't have 10 days of no games for my Switch.
Did anyone else have a similar issue, and have it fixed?