No, the timetable doesn't work. Development of TNG overlapped with the production of The Voyage Home considerably. TNG was a reaction to Star Trek II and Star Trek III that rode the publicity wave of Star Trek IV and the 20th-anniversary. It was after Star Trek III that Paramount decided they wanted a new Star Trek series. They asked Harve Bennett to produce and he passed. They asked Nimoy and he passed. They asked Greg Strangis, and Strangis said yes. (The little we know of Strangis' work is documented in David Alexander's Star Trek Creator; riffing on Star Trek II, it was apparently cadet-centric.) In any event, Roddenberry came in late to the process; either Paramount found Strangis' proposal unworkable or Roddenberry made a political move to get himself dealt back in at the table and Strangis shown the door. While Roddenberry's work on TNG began in 1986, the intent by Paramount went back well before the film. It's only the coincidence of the calendar that makes it appear that TNG was a reaction to the most recent of the films at the time, Star Trek IV.