You can not be the reincarnation of someone who is alive at the same time you are. Stanley Kubrick puts a clue in the dialogue that proves Jack in the present day Overlook could not in any way be a reincarnation of Charles Grady (who killed his family and himself) or Delbert Grady (the putative “ghost”).
Listen to the bathroom conversation between the two, Charles Grady and Delbert Grady appear on the surface to be the exact same person, but they aren’t. Delbert Grady is lying to Jack when he tells him his name as we know from the interview his real name is Charles Grady. Delbert and Charles are two different entities. One is a real person and the other isn’t. "Remember what Mr. Hallorann said. It's just like pictures in a book, Danny. It isn't real.” Delbert Grady is a vision that looks exactly like the real Overlook caretaker Charles Grady, but they are not the same person. We know this positively from the dialogue Stanley Kubrick put in the movie. Jack says this as he talks to himself in the bathroom, “Mr. Grady. You were the caretaker here. I recognize ya. I saw your picture in the newspapers.” There’s something here that movie viewers who have never read the novel are not aware of. When Jack says, “I saw your picture in the newspapers” he's referring to the very important unexplained scrapbook that we see open on his desk throughout the movie (The scrapbook plays a big part in the novel as it’s in the basement and used by “the manager” to lure Jack. It contains articles about the hotel's less savory guests and Jack eventually decides to use it to work on a different project apart from the play he was working on, about The Overlook’s past). In the movie Jack knows exactly what all of the previous hotel guests, who aren't "all the best people", look like after he opens up the scrapbook. The book is just as important in the film but we don't realize it at first.
When he says, “I saw your picture in the newspapers” he already knows what Charles Grady looks like. You don’t know what Grady really looks like, but Jack does. Delbert Grady, “the ghostly vision”, and Charles Grady, “the caretaker”, look exactly the same and Jack is the only one who knows this for sure. He’s imagining talking to the person he idolizes, the same Charles Grady that he’s seen in the newspaper clippings who killed his family and himself in 1970. The major problem is this; there can’t be any reincarnation of these two people (“You have always been the caretaker”) because of what we're told in the interview by Mr. Ullman. The two little girls were killed in 1970. Jack and Charles Grady, when he worked at the hotel, were both alive at the same time. Grady’s lying when he says this line to Jack in the bathroom conversation “You are the caretaker, you have always been the caretaker” as they were obviously both alive at the same time in 1970, and are two entirely different people. This can’t be debated or changed no matter what your opinion is. Again, you can’t be the reincarnation of someone who is alive at the same time you are.
Stanley Kubrick even tells us in the dialogue that Delbert Grady "isn't real", and this should be no shock as he along with the rest of the party goers are all a vision we’re seeing from inside Jack’s imagination. It's all because he’s looked at their pictures in the scrapbook. Again Stanley Kubrick points us to this in the dialogue, “Remember what Mr. Hallorann said. It's just like pictures in a book, Danny. It isn't real.”