Ahh! It works! I made the php location too complex and realized where it was bombing after getting a 404 on submit. It was much, much more simple than what I had. Between the 404 and reading in the page that Cliff linked me to (or maybe one of the pages linked there), it said that most people try to do too much with index.php and that /index.php usually works. It most certainly did. I'm thrilled.

location ~ \.php$ {
try_files $uri /index.php =404;
fastcgi_pass unix:/var/run/php-fcgi.pid;
}

Also, the "internal" reference worked before, but that had to be removed... maybe it was working due to my browser's cache? No idea.

Now, time to tweak and optimize. Thank you for your help!