OT: WordPress File Disitribution

This is totally off topic, but I’m not sure where else to turn on this one:

I run https://www.junkylife.com, which is a centralized location for bloggers to blog about their daily opiate-addicted, recovered, or recovering lives. I have about 30 members and each member has a blog off of the junkylife.com domain.

The solution I’m looking for is a way to update the wordpress, plugin, or theme files of every single blog without having to browse to each folder and copy/paste (for instance, one of the themes I have installed for each member was broken. After fixing the header.php, I would have to manually browse to the folder name and drop the header.php into each blogger’s theme directory.)

My solution so far has been to just copy/paste the file(s), including empty directories, however many levels deep, to avoid having to browse to each sub-sub-subdir.

Does anyone know of a way that I could automate this process? Some type of synchronization, etc?

Thanks in advance for any help with my ‘off-topic’ question….