You can sometimes get original keys from ebay alot cheaper.
If the Mhz is correct BMW should beable to code it !
You would have to get the metal as a blank and cut though.
It's probably best to just bite the bullet with BMW as the key will be cut to your car.
Not sure if they charge to code it in the price. Worth asking.
I'd be on to the garage and tell them to pay BMW direct for a replacement key or give you some money back.
D3 MT - #612 in Montegoblau