I believe the short answer is there is No way for you to update a composition without opening each project file and replace the composition manually.
my workflow would be this:
1. open a project and reduce project of that composition
2. make the change and save the file as just this composition project file
3. open a project file and import the composition, and in the project window drag with ALT key pressed the new comp on top of the old comp.
4. repeat step 3 x 9 times
if you need to setup a situation in the future when you know you need a dynamic change in a composition inside, and don't want to use the method above, you can use a rendered video file in those projects, and use a project for just that composition and render to a folder that each project takes this footage from.