I've not tried this, just trying to think outside the box...
So say you take just one track, extract a tempo map/make a groove clip , then save that project as "tempo map"
Then save the project as "track1".
Then, set the tempo to some average so that everything is the same tempo (e.g. if the tempo range in the map was between 115 and 125, you'd set the tempo for the whole clip to 120).
Then save the groove clip as "clip1".
Now start a new project, "track2" with the second wav file, extract a tempo map/make a groove clip, set the tempo to the same as clip1 and save the clip as "clip2"
Do the same for the other three tracks.
Then open the original "tempo map" project and drag each of the saved clips into the project as new tracks.
So basically you're:
1. Getting a map of the tempo for the song from one of the tracks.
2. Evening out the tempo of all the tracks to a fixed tempo, saving each track as a groove clip
3. Importing them into the original project, so that the original song tempo map (with all its variations) is applied evenly to all tracks.
There's probably some work involved in setting the fixing the time-markers when creating the groove clip, but wouldn't something like this work?