Logging in to WordPress from Rails

I have a rails app (v4.1.6 at the moment) that uses Devise. I have
configured a subfolder to serve up WordPress for a blog. That is:

http://my_app.com --> rails app
http://my_app.com/blog --> wordpress

That is all working great, but I also want the user to be logged in to
wordpress when logged into the Rails app.

I did this years ago by having the wordpress server send a request to
rails app using the browser’s cookie. At some point (I forget, maybe
3.1?), Rails got smart enough to figure out that the cookie wasn’t
from the browser and it invalidated the session.

So, now I’ve got the same business need and am looking for a solution

Is there a way to get Rails to not invalidate my session when I reuse
cookie from the server? I’d like to create a new action
that I can call from wordpress. If I can relax the rails security for
that call, I think I can do the rest.

(There’s a plugin https://wordpress.org/plugins/rails-integration-api/
looks like it would be perfect, except for the part that it is no longer
maintained, doesn’t work, and the developer’s website is gone.)