I propose that the difference in T1 and NT+T2 is one of intent.
T1 begins words and structures. The intent is to get students to acquire specific words/structures.
T2 begins with a message. The intent is to get students to acquire more data to build interlanguage on their timeline.
Therefore what we would want to do is get teachers to do is begin with meaning as Ben said. Begin with the intent to communicate.
Words/structures are the basis of T1. Many TPRS teachers build stories around word lists, from high-frequency word lists, district/textbook word lists, or words that they backwards-planned from a novel. T1 is alive and well in TPRS because word lists and targets and massed repetitions (via circling) are demonstrated to the teachers in trainings. Students see daily target structures written on the board and the goal is to repeat them many times during the lesson. The focus is on the words more than the meaning.
Messages are the basis of NT + T2. There are many ways to deliver this kind of input. TPRS stories created without target structures and with a lighter touch at circling, with a lighter urge for 100% transparency, with the “illusion of transaprency” as the goal. We also have many other flavors to choose from. Just to name a few, we have Beniko’s Story Listening and comprehensible novels read for SSR and Read and Discuss, and Movie Talk the way it was originally devised, and Look and Discuss when the intent is to simply discuss the contents of the image, and Ben’s Invisibles stories, and activities like origami or Simon Says or Annabelle Allen’s OWL-inspired Brain Breaks, or discussing the calendar/weather and school events or any of the fine strategies that Justin Slocum-Bailey wrote about in the IJFLT recently can be the basis to provide NT + T2 input.
There might be reference posters on the wall, e.g. colors, numbers, weather words on the calendar, maybe a poster of the “high frequency” words that come up again and again. These would be there to simply save time when the words printed thereupon were needed. However there would be no “structures of the day” posted in the board that the teacher planed to use in a massed way. This is because the intent is to communicate a message: spin a story for the kids, fold some origami, find out others’ opinions on the calendar/weather, play Simon Says, etc.