I tried again, this time trying to capture at the moment when I'm transferred
from the login domain to the content domain (where I assume the temp cookie is
being set).

This time I got a page from the proxy after the capture saying that a response
had been captured (with a Back link). Using the back link gives me an access
error from the content domain.

I have a feeling that there is at least one redirect between when I click from
the login domain and then I get to the content domain. If that first redirect
does not set the cookie, then the capture won't get it.  (I really need to
capture the server response to the request generated by the redirect)

Does this sound correct? If so, is there a way to capture that subsequent
response?