Custom rewrite rule for backend/admin?

I would like to create a custom rewrite rule that will take the URL:

http://domain/submit-project/add

but display

http://domain/wp/wp-admin/post-new.php?post_type=project

Is there any way to do this? I am trying to add the rewrite rule so in my theme’s functions.php

add_action( 'init', 'add_custom_rules' );

function add_custom_rules() {
  add_rewrite_rule(
    "^submit-project/add",  
        "/wp/wp-admin/post-new.php?post_type=project",  
        "top");
}

I’ve tried flushing the rules, but this always seems to enter some kind of loop always going back to the ‘login’ page.

Edit

1. The URL is actually just 404-ing now
2. I should add that I do have a page with the slug submit-project and thus the URL: http://domain.com/submit-project in case it matters.
3. I’ve installed the plugin Rewrite Rules Inspector and can’t seem to find my rule in there.

In general, it is possible, but you need to define ADMIN_COOKIE_PATH in your wp-config.php to the value / which might cause security issues.

First of all define this rewrite rules in your .htaccess right before the rewrite rule of wordpress:

# Make sure, there is a trailing slash
RewriteRule ^submit-project/add$ submit-project/add/ [R=301,L]
# mask the urls
RewriteRule ^submit-project/add/$ /wp/wp-admin/post-new.php [L,QSA]
RewriteRule ^submit-project/add/post.php?$ /wp/wp-admin/post.php [L,QSA]
# this is the wordpress rule:
RewriteRule . /index.php [L]

Now you need to define the constant in the wp-config.php

define( 'ADMIN_COOKIE_PATH', "https://wordpress.stackexchange.com/" );

I recommend not to use this on a productive site. Consider to offer a special input formular in the frontend using shortcodes or something less invasive than the shown example.