I had a flight for early May that SW has been moving around multiple times over the past 3 weeks. I've been watching it in my account, more curious about what the end result was going to be than I was interested in cancelling it myself. For 3 weeks, my account showed the flight in various stages of change and I've been unable to make any changes to it myself; I'd get an error and a message that I needed to call SW. On Monday night, I got an email from SW that my flight had been changed and that I could change it if I wanted to. Checked the app, and sure enough, I could now make changes to the flight. I didn't do so, though. On Tuesday, I got a call from SW (it went to voicemail) informing me of the change and offering me the opportunity to change the flight or get a full refund.
Yesterday, I decided to go for the refund, and called SW. The first two minutes of the call was all the recorded announcements about high-call volumes, how I could make changes on the website, and how I could have them call me back. I chose to just stay on the line - curious to see what wait time was. After another message warning me of high call volumes, I was finally informed that my wait time was less the 2 minutes. The phone rang once and was immediately picked up by Cindy, who was about as pleasant and efficient as humanly possible. She processed my refund quickly (4-7 business days until it shows up in my bank account). I had EBCI on this flight, and while she was not able to directly refund that herself, she started the transaction and sent it off to the appropriate team that would be able to initiate the refund. I had an email notification for each of these transactions before I even hung up the phone. Cindy warned me that the email was the generic "your refund is in the form of Travel Funds" email, but not to worry, the refund had actually been processed.
So if you need/want to call, don't worry too much about lengthy hold times - that doesn't seem to be the case at the moment. YMMV
Steve