But later I discovered they were all syncing to a tempo track that had multiple or various tempo adjustments through out the lenth of the song rather than, what I want, one consistent tempo for the entire song.
If you did the tempo detection right, and everything is in sync, just disable the tempo track (change the transport from follow tempo to fixed tempo).
If your audio events are in musical mode, now they should follow the fixed tempo. If you select an audio event and choose Audio/Bounce selection, you will get a new event with the fixed tempo embedded.