Variable bpm for movie

You painted yourself in a corner, but that happens to pretty much everyone on their first score in logic.

It is not advisable to have more than one cue in a project for the very reason you found out. Every tempo- or signature-change you do affects all events downstream.

Now, you could SMPTE-Lock any of those following events, which would indeed lock them to picture even when you change tempo upstream, but consider this: by changing tempo, you move the grid underneath the locked regions. So what was perfectly on the beat will certainly not be there anymore. You may say you are willing to accept that, but good luck if the director asks for changes (hint: he will). Also, if you worked with tempo dependent FX, those will adapt to the new tempo, so delays or filter wobbles will be out of time.

Use one Logic project per cue (use Save As... without assets so they all share the same project folder) and then one master project at 120bpm where you line up all your mixes or stems at their correct time codes. Makes it easy on managing revisions ("...you know, the mix you had previous to the last one that we asked for two weeks ago...") as well. Also, this will be the source for the AAF you export to the dubbing mixer after final approval. No one wants to manually line up a bunch of individual wav files one by one to a time code list.