To fill the space as you mentioned, how thick should the piece of wood be? Would I nail it in and put glue along the edges? Just want to make sure I install it securely since the track will be on it. Thanks!
You really need to check the new doors to make sure you don't actually need to remove more wood.
To fill, you need a piece cut with minimal gaps. I would glue and nail it in place.
Spackle the cracks and sand smooth.