I am working on a text adventure game which will have at least a few components (a text area for narrative and text input for user input) on the stage at all times. Therefore, I
The fact that they will be on stage at all times shouldn't stop you from creating specific classes for them.
Depending on your game structure, you could either create a MovieClip with your TextFields and link them to the Typewriter class, or simply create a class for the TextFields and use Events to modify the text content.
You're using external classes so there are no reason to keep any kind of logic inside Flash CS.