How to install WordPress alongside Laravel on Ngin

I have a Laravel site running on Nginx, and it's fine.

It has a normal folder structure like:

/app
/public
/vendor
...

The /public folder is where the Laravel index.php is.

I've installed WordPress at /public/blog because I want my blog to be visible at mywebsite.org/blog.

The blog currently works fine if I leave the Permalink Settings defined at /blog/wp-admin/options-permalink.php set to "Default" (which means the URLs for posts look like /blog/?p=123). If I change Permalink Settings to /blog/%postname%/, I can't view the posts (I get a Laravel 404 page).

I definitely want my blog posts to have SEO-friendly URLs (pretty permalinks).

My current Nginx config is:

server {
    #This config is based on https://github.com/daylerees/laravel-website-configs/blob/6db24701073dbe34d2d58fea3a3c6b3c0cd5685b/nginx.conf and seemed to be necessary to get Laravel working.
    server_name mysite.local;

     # The location of our project's public directory.
    root F:/code/mysite/public/;

     # Point index to the Laravel front controller.
    index           index.php;

    location / {
        # URLs to attempt, including pretty ones.
        try_files   $uri $uri/ /index.php?$query_string;
    }

    # Remove trailing slash to please routing system.
    if (!-d $request_filename) {
            rewrite     ^/(.+)/$ /$1 permanent;
    }

    # Yoast WordPress SEO plugin says to add these 2 rewrites:
    rewrite ^/blog/sitemap_index\.xml$ /blog/index.php?sitemap=1 last;
    rewrite ^/blog/([^/]+?)-sitemap([0-9]+)?\.xml$ /blog/index.php?sitemap=$1&sitemap_n=$2 last;

    # pass the PHP scripts to FastCGI server listening on 127.0.0.1:9123
    location ~ \.php$ {
        fastcgi_pass   127.0.0.1:9123;
        fastcgi_index  index.php;
        fastcgi_param  SCRIPT_FILENAME  $document_root$fastcgi_script_name;
        include        fastcgi_params;
    }

    location ~* \.(css|js|gif|jpe?g|png)$ {
        #images, CSS, and JS have 1 week expiration: http://aspyct.org/blog/2012/08/20/setting-up-http-cache-and-gzip-with-nginx/ See also: http://serverfault.com/questions/339240/chromium-audit-says-its-not-caching-static-content-yet-headers-are-set-who-i
        expires 168h;
        add_header Pragma public;
        add_header Cache-Control "public, must-revalidate, proxy-revalidate";
    }

}

I have spent hours reviewing other answers (listed below) and haven't figured out how to get this working.

Suggestions?

https://stackoverflow.com/a/10089936/470749
https://stackoverflow.com/a/18596822/470749
https://stackoverflow.com/a/17816122/470749
https://stackoverflow.com/a/12635095/470749
https://stackoverflow.com/a/11522602/470749
https://stackoverflow.com/a/6155935/470749
https://stackoverflow.com/a/23416206/470749
http://codex.wordpress.org/Nginx#WordPress_Multisite_Subdirectory_rules
http://codex.wordpress.org/Giving_WordPress_Its_Own_Directory
https://rtcamp.com/wordpress-nginx/tutorials/multisite/subdirectories/in-a-subdirectory/

P.S. I'm flexible with where I'd install the WordPress files (e.g. either at /public/blog or move it up a level to /blog or /wordpress).

You route everything to laravel in your / location, but you need to write everything /blog/ to the index.php in /blog/index.php:

location /blog/ {
    try_files $uri $uri/ @wordpress;
}

location @wordpress {
    rewrite /blog/ /blog/index.php;
}

Then your php handler needs path info support:

location ^/blog/index.php(/.*)?$ {
    fastcgi_split_path_info ^(/blog/index.php)(/.*)$;
    fastcgi_pass   127.0.0.1:9123;
    fastcgi_index  index.php;
    fastcgi_param  SCRIPT_FILENAME  $document_root$fastcgi_script_name;
    fastcgi_param  PATH_INFO $fastcgi_path_info;
    include fastcgi_param;
}

Turn on debug verbosity for error log if this doesn't work and post log info.

UPDATE: Note from original question asker:

Here is a snippet of my new Nginx config, which seems to work for these URLs: /, /blog, /course, /blog/innately-happy, and /blog/sitemap_index.xml

...
error_log /Users/myuser/code/myproject/storage/logs/nginx_error.log debug;

 # Point index to the Laravel front controller.
index           index.php;

location /blog/ {
    try_files $uri $uri/ @wordpress;
}

location @wordpress {
    rewrite /blog/ /blog/index.php;
}

location ^/blog/index.php(/.*)?$ {
    fastcgi_split_path_info ^(/blog/index.php)(/.*)$;
    fastcgi_pass   127.0.0.1:9000;
    fastcgi_index  index.php;
    fastcgi_param  SCRIPT_FILENAME  $document_root$fastcgi_script_name;
    fastcgi_param  PATH_INFO $fastcgi_path_info;
    include fastcgi_params;
}

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