Here's a tip: ust say "OK I understand, but in the meantime could you please make a new reservation for me and put it on hold?" Make a "fake" one and make sure you get the confirmation number. Hang up. Call back and ask for a supervisor/manager saying "it's regarding an agent that I just dealt with. . ." Give the fake confirmation # - they're able to track the agent even if you didn't get their name. Make your complaint and that solves your problem of wanting to complain.
On the other hand, the 1K agent was right - there are certain things they require web support for. Not sure that's "poor service" more than inefficient. Why don't you just take screenshots (use fullshot or some such program) and then send them all in via email to UA for your voucher? More work; less aggravation.
Also, I'm not sure that one anecdotal experience is cause for the "sky is falling" attitude that some others have posted here. . .