Sorry, I do not have any personal magic for dynamically attaching a Folder Action to a newly created folder from an existing Folder Action. 😟
Maybe someone else has some ideas.
If time is not critical, AND the Folder tree is not HUGE, you could create something that wakes up every so often and just applies a
chmod -R ...your.stuff.here...
to just brute force the changes.
But if the interval was too frequent, or the size of the Folder tree was too big, you could be putting a lot of CPU and I/O load on your system that might interfere with normal operations.
I guess if you want to try and attach folder actions to new folders, you could figure out what kind of .plist is created and stored in what directory, then dynamically create a new plist and attach it using the launchctl command. Technically I think it could be done, but I have never tried it, so I don't know what the .plist would look like, nor where it would be stored, nor what the launchctl command to enable it would look like.
And if you are going down this path, you would have to keep in mind what happens when a given sub-folder was deleted. How do you clean up all the folder action scripts you created that no longer have a object to monitor?
But if you want to go down this path, then warm up your "Google Foo" and start researching.