My understanding is that DL can handle e-ticket for the infant-in-arms (when required for international trips), but some others can not. And I assume the pax is not on all DL metal.

Is kind of bizare that such tech still does not exist.

OP: I assume it will not take two full weeks, just a CYA. I would also not be that worried about the cost. It is something like 10% of full fare, so they can not say the cheap fare is not available.

EDIT: On second thought, perhaps they send it by Pony Express and it will take 2 weeks to get to the west coast. You might want to send them a telegraph and confirm :-)