You should try contacting SW via Facebook Messenger. I used it earlier this year to add my infant to our flight and it was super fast.
I have also used the text to customer service on a couple other things that has been way more helpful than sitting on the phone for hours. For instance, we had to change our Maui flight 3 times during the pandemic (flying Hawaiian Air), and they were able to do everything over text. Plus they respond immediately with a time estimate for when you will get a rep to text you back. Then you can go throughout your day and just wait for the text.