I have my initial greeting set as NOT INTERRUPTIBLE! But when I test it in a live environment I am finding that if I press a TT during that message it skips the next PLAY step before the GET TT step. It finishes playing the initial greeting but not the next.

The interruptible setting on a Play step simply indicates whether that play should be terminated by a Touch-Tone. It does not control the Touch-Tone input buffer, which will still gather the TT input and save it for later processing. In order to achieve the functionality you want, place a Clear step immediately after your initial greeting.