Mishman7

В итоге, рабочий location в моём случае:

location ^~ /wp {
root /var/www/mysite/mysite_rest;
index index.php index.html index.htm;
try_files $uri $uri/ /wp/index.php;

location ~ \.php {
    fastcgi_split_path_info ^(.*\.php)(.*)$;
    include fastcgi_params;
    fastcgi_param SCRIPT_FILENAME $document_root$fastcgi_script_name;
    fastcgi_param PATH_INFO $fastcgi_path_info;
    fastcgi_param PATH_TRANSLATED $document_root$fastcgi_path_info;
    fastcgi_pass 127.0.0.1:9000;
}

НО ПРИ ЭТОМ было убрано rewrite ^/(.*)/$ /$1 permanent;