While Audition can work with Video, I’d use an NLE for laying out the work. Vegas, Premiere or Final Cut Pro on a Mac would be better suited for the work.
That being said…
In Audition just setup one audio track for each voice artist. Label appropriately. Save all files to a single directory/folder along with the Audition project file. After each days work, I’d zip it up and save off to a thumb or hard drive.
Keep all the previous work so you can go back if disaster strikes. A written log of where you are at for each days work always helps. Forethought will save you in the end.
Just a note…
Never change file names outside the program you are using them in. If you are going to use an external program with any audio file to alter the audio, be sure to maintain the bit rate and bit depth. Id always keep a backup of the replaced file and note it.
Good Luck
Steve