I was able to solve this problem by executing the following (in Javascript) when the user clicks the button indicating that they wished to join the call:
audioElement.pause();
audioElement.play();
From my research, it seems that Safari on iOS is very protective of unsolicited audio being played, requiring that sounds be a direct result of some kind of user action (e.g. a button click). This code in the event handler makes sure that the audio is enabled even though the user actually joins the call much deeper in the code.
