Custom rewrite rule for backend/admin?

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.