You are doing a great job with Tiny Core. I am sure, some of the things I suggest, you were planning to implement anyway, and you have different ideas for other things.
Now you have Update Dep Database, which adds new dependencies to .dep files, and affected programs won't start.
You have Display All with Missing Dependencies, so we know what is missing.
The next logical step is to have "Install Missing Dependencies."
You could also have the option of including this with TCE Update.
This keeps it simple for new users.
You were probably planning this before I suggested it.