How to change tempo without affecting the music (only the grid)

This is a very basic problem. I have been laying songs (audio files) onto logic and recording vocals over them, and now that I am finished with the recording, i realize that in order to copy and paste the choruses EXACTLY throughout the songs, which can be quite arduous the way I have been trying to do it, one needs to have matched the proper tempo with the the music being used.

I neglected to do this at the start of these projects, and it has come back to bite me because when I try to change the tempo now, it completely throws my vocals out of whack because my voice is off beat. This is where the problem lies. I know had I addressed this at the beginning, I would be smooth sailing.

I also tried setting the tempo at the proper rate on a new logic project, but when I drag everything over from the original project, the same problem occurs.

In reality, I need the grid to match up so I have the proper means to line up my vocals exactly so the choruses are consistent throughout the song (obviously I can do it manually in a way regular listeners might not notice, but Im dissatisfied with that, I want it to be perfect)

Again, I know that if I had matched the tempo properly with the audio file (the music) at the beginning, there would be no problems, and I'd be able to record over it and then use the bars to align my vocals perfectly.

If some one would be so kind as to get back to me on this, it would be highly appreciated