Redirect loop with Wordpress on Apache with nginx reverse proxy and HTTPS on Ubuntu 16

I’m experimenting with a DO droplet to host my Wordpress blog, setting it up myself because I’m difficult that way.

I configured Apache with TLS via Lets Encrypt and migrated my Wordpress blog over, and everything was working fine.

I then put nginx in front of Apache as a reverse proxy and configured nginx as the TLS terminator, redirecting any non-https to https using the tutorials here.

Now I can access any static files which are served up by nginx, and accessing a phpinfo() test file on Apache works fine. But accessing any Wordpress php files, like index.php or admin triggers a redirect loop.

What did I do wrong? Here’s my nginx config

# Default server configuration
#
server {
        listen 80;
        listen [::]:80;
        server_name demo.EXAMPLE.com;

        # redirect all http to https
        return 301 https://$server_name$request_uri;
}

server {
        # SSL configuration
        listen 443 ssl http2 default_server;
        listen [::]:443 ssl http2 default_server;
        include snippets/ssl-demo.EXAMPLE.com.conf;
        include snippets/ssl-params.conf;

        root /var/www/demo.EXAMPLE.com/public_html;

        index index.php index.html index.htm;

        server_name demo.EXAMPLE.com;

        location / {
                try_files $uri $uri/ /index.php;
        }

        # proxy PHP requests to Apache
        location ~ \.php$ {
                proxy_set_header X-Real-IP  $remote_addr;
                proxy_set_header X-Forwarded-For $remote_addr;
                proxy_set_header Host $host;
                proxy_pass http://127.0.0.1:8080$request_uri;
        }

        # deny access to .htaccess files, if Apache's document root
        # concurs with nginx's one

        location ~ /\.ht {
                deny all;
        }

}