Take a look here:
https://docs.moodle.org/34/en/Managing_authentication#Alternate_login_URL
In theory you should be able to implement custom local plugin that would host your custom design and logic.
https://docs.moodle.org/dev/Local_plugins
Than you would configure the Moodle to point to your script in that local plugin.
If you visit the settings page on your site - http://mymoodle.url/admin/settings.php?section=manageauths
You will see the settings and following explanation:
If you enter a URL here, it will be used as the login page for this site. The page should contain a form which has the action property set to 'http://mymoodle.url/login/index.php' and return fields username and password.
Be careful not to enter an incorrect URL as you may lock yourself out of this site.
Leave this setting blank to use the default login page.