When UA screwed up a refund for me, I had to call the refund department 7 times and they never were able to fix the issue. They told me multiple times that they'd call me back but the call never came. It took a DOT complaint to fix the issue.

If refunds doesn't return your call, I'd recommend just filing a complaint. At least that way, you know that the issue will get taken care of in a reasonable amount of time and effort.

If you want to give UA the benefit of the doubt before filing a DOT complaint, use the webform.