Nothing got to do with A records or what so ever
If you insist on what you’re trying to achieve, you got few options:
cp /var/www/htdocs/index.html /var/www/htdocs/index.html.BACKUP;
sed -i 's/\/UI/\/ftp/' /var/www/htdocs/index.html;
WARNING, you’ll then need to access your MyCloud Dashboard by manually appending the path i.e. http://192.168.1.x/UI because it now redirects to /ftp by default. If you know HTML/JS you could easily make this file route to your desired paths This is the easiest method without knowing CGIs.
2. Add another port listener directive like you mentioned and forward the appropriate port on your router. Don’t forget to restart Apache2. But if your router doesn’t support PAT (Port Address Translation), you will then have to access via the not so good looking ‘domain:port’
3. Modify to use virtual host directives. I’ve done this before in the past to host multiple websites on MyCloud’s Apache2 but now I’ve switched to the faster Nginx+PHP-FPM