I just now found this post about a system that might do what you want. You basically blog by email — except you replace the existing wp-mail file with a special one that doesn’t delete the email after it’s read.
You can then have other blogs read the email and post the message.
This person recommends setting up a cron job to make it automatic.
I’ve been doing some blogging by email (not using this system) and find that most email clients will wrap your messages at 60 characters, which can mess up your posts (especially if you include links). I’m going to experiment with RoundCube; from some very limited tests, it doesn’t seem to wrap at 60 characters, so I’m hoping it won’t mess up my posts.
Again, a disclaimer: I have not tested this system, I do not know if it works or if it is safe; it is simply something I found five minutes ago while searching for the answer to another wp-mail isse, so perform due diligence before implementing:
https://www.justin-cook.com/wp/2006/12/06/post-to-multiple-wordpress-blogs-by-email/
–Tom