You are not delusional, but you are wrong. UA's sole obligation is to refund your tickets. Some specifics:

1. Call UA during the regular business day in the US. Ask the GS agent to contact TG to ask TG to open award seats. This will go through a UA and TG liaison agent and is manual and takes a couple of days. There is nothing UA can do other than ask. It's a long shot, but it happens.

2. Look at other *A routings and propose those in order of preference. As others note, this may involve an overnight somewhere. Even if it ultimately comes to pass, it is better than the alternative.

3. Are there routings which might involve a paid segment on a non *A carrier such as an LCC? These have risk because separate tickets means the risk of a noshow is on you.

Just keep plugging, but don't expect UA or any carrier to do the lifting for you.