Actually i think this company should rename + remake the drama.
Simply just rename the titles, and change the story backgrounds and character into another fictional names.
And for all the Korean people there, hopefully you think this issues in a positive ways. Drama are always drama, and it just an entertainment things. The whole world know that contain in this drama aren't real nor anything to do with Korean's Joseon history.
Please think this positively.
Instead asking the drama to prove the background story in this drama were real and happen in history;
Why not you try prove one drama on whole year of 2020-2021 is REAL and without fictional elements contain in the dramas?
If a drama that 100% without any fiction contain in the "drama", that wasn't a "drama" ; that story is call "Documentaries".