Why would you want to set Firefox as default browser in the first place? In other words, what are you doing that requires you to set a default browser? If any action requires to specify an app as default app Android will prompt you for it. You can then permanently choose Firefox for that action.

The issue was that Chrome is automatically set to the default by the OS, since its a built-in app. There appears to be a glitch where additional browsers do not get added to the choices if a default is currently set. I cleared the default via Chrome app info, which allowed me to then select Firefox via the prompt as you suggested. It also added Firefox to the list of browser choices.