The large cap-with-nut thing with the spring and thimble shaped screen behind it - are notorious for rounding off because they are tightened too much, and made of junk metal.
All the above suggestions are on the list....along with the reminder that it is delicate metal. It can split, break or ? if you get too frisky with it. Scooter shops are used to dealing with it.
Also, bear in mind....95% of us never find anything in that screen worth worrying about. Some folks never remove it after initial engine run-in -- for just the reason you are experiencing!
So, use the other drain to renew your oil....and don't worry about that other thing. Just a thought.
If you do get it off, these GY6 things (with rubber O-ring, screen and spring) sell for a couple bucks on ebay. I keep a spare kit.
Stig