Thanks for your response! I know there has been one post on the same issue (which I referenced in my opening post), but I haven't seen anything regarding the discussion that I describe with the United rep when I called Reservations, which you have suggested I do.
From your answer, I glean that being in the queue for ticketing shouldn't be a cause for concern, because I will receive a ticket within 24 hours or I will be able to call UA and get them to issue me a ticket while I'm on the phone.
My lingering question, however, is whether the claims from the UA Rep that forcing the ticketing within the 24 hour timeframe could create problems for me in some circumstances when I travel on this ticket. Any information in regards to this would be useful for me and for future travelers.
Thanks!