First, as always, when an author uses straight quotes from an episode or book, the material must be given proper citations, i.e.: Harry Potter, Goblet of Fire, p. 56., Star Trek: The Next Generation, Episode 11, etc.
That being said, there is a distinct difference between quoting material and these ReadTheBook or FanMake type stories.
To escape the label of ReadTheBook or FanMake, a story must contain substantially more original written material from the fanfiction auihor than straight copying of the rightful owners' scripts or stories. Simply adding author's asides will not suffice. Simply changing the characters names will not suffice. Simply adding a new character to speak in a narrator's voice, etc., will not suffice. Finally, the one that completely baffles me: simply changing the universe, say turning Lilo and Stitch into Rizzolli and Isles, will not suffice. The key word is substantial.
What is concerning is your statement, "I changed things up a bit of course, sometimes adding things ..."
I am not certain that simply changing things up "a bit" will meet the criteria for substantial. Without seeing/knowing the episode/script and your version, I cannot say with any confidence whether or not the story qualifies as a FanMake or ReadTheBook entry.