Brazil
Hi 787,
Most flights from Europe route southwest near the Canaries/Cape Verde islands, diverting to the USA would nearly be as far as flying back to Europe!
However please don't go against your company policy but they are being a bit ott if this is what they insist on. If you do end up entering the US then you do need a crew visa, the visa waiver program is for tourism and short biz trips only.
If your flight had a MAJOR tech problem, you could expect an overnight in Lisbon, Tenerife, Sal, Dakar or Belem.
Enjoy the beaches!