I didn't expect it to be easy. I also didn't expect it to be impossible.

How does R availability work? Does United allocate a certain number of R seats for each flight, and when they're used, that's it? Or do some flights never even get R seats to begin with?

If it's the first process, it does seem suspicious that there literally isn't one R availability on a random Sunday in March from SGN, routing through anywhere. Do you really believe that everything with United is on the up and up?