It looks like you've painted yourself into a corner somewhat. In order to make the best of your situation as painlessly as possible, why not try this:
1. Open your source project that contains multiple songs. Let' say one project contains Song A, B, and C.
2. Do a "Save As" and call it Song A. Delete songs B and C from it.
3. Go back and open your original source project, do a Save As, and rename it Song B. Delete Song A and C from it.
4. Go back and open your original source project, do another Save As, and rename it Song C. Delete Song A and B from it.
Now you end up with a separate project for each song. And your tempo maps are in place with each song, although they don't all start at the beginning of the project. You could just leave them as is and work with them wherever they fall in the timeline. There's nothing wrong with doing this.
If you did want to re-align them all up so they begin at the beginning of each project, you should be able to move the tempo maps from within the tempo window without too much difficulty. Select all events and then just mouse drag the position of the first event to the location you want, and everything should be intact. You could do the same with time or key signatures if necessary. And you could drag the regions over manually, or via the Event List if you "go up" one level so that you can access all the regions.