Dueling DNS Dillema

[david-8uUts6sDVDvs2Lz0fTdYFQ at public.gmane.org (David Kramer)]

As some of you know, I am also on the board of
http://www.agilebazaar.org, as well as the Team Lead of their IS group.
 We are in the process of changing names from New England Agile Bazaar
to Agile New England.  Due to my particular brand of insanity, I am
trying to combine moving web hosts at the same time as the name change.

We are currently on GoDaddy, a company that I have defended in the past.
 We've had a lot of problems with their service, only made more
frustrating by their refusal to acknowledge the cold hard evidence I've
given them in the way of diagnostics output from a watchdog program I
wrote (more info on request).

We did our research, and selected HostGator as the new web host.  While
we haven't gone live their yet, I am outright giddy over how good their
24/7 chat support and service is.  I highly recommend them.  We're still
fighting Joomla a bit, but that's not their doing.

Here's the problem.  The new domain names were bought by another member
of the group, under a personal GoDaddy account she controls, separate
from AB's own GoDaddy account, which I hope to soon take great pleasure
in canceling.

The process to transfer the domain name from her GD account to our HD
account starts with her getting the auth code for the website from GD,
and us filling out an online form on HG.  A few hours later she gets an
email asking for confirmation, and that's pretty much it.

The problem is every time we get the auth code and try it, a few hours
later we get an email back saying the auth code was wrong.  We have
tried this no less than seven times.  Oh, and we tried the "wait a few
days and try again" thing in case the responses to onld requests were
getting mixed in.  No joy.  Not even a Betty.  Both companies say it
usually "just works", and they don't really hav a procedure for doing
sensible things like TALKING TO EACH OTHER!!!

What would you do in this situation?
Thanks.