Why isn't my Nginx try_files directive working to remove an extension

My site is a basic PHP site with a WordPress blog installed in a subdirectory. I need to use pretty URLs, so I need to remove the .php extension from the files in root, and then get WordPress to behave like WordPress in the /blog subdirectory.

I've only been able to get one to work at a time and can't figure out what I'm doing wrong.

This config works for WordPress, but downloads the .php files in root. :/

location / {
    try_files $uri $uri/ /$uri.php /blog/index.php?$query_string;
}

UPDATE

I've added a separate location so now the extension removal is working in root, but the blog links just go back to the site's home page

location / {
    try_files $uri $uri/ $uri.php;
}
    
location /blog {
    try_files $uri $uri/ /index.php?$query_string;
}

// also tried this, with the same results
location /blog {
    try_files $uri $uri/ /index.php;
}

Figured it out. I needed to add /blog/ as a path inside the /blog /location

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