I am pretty sure that Shulchon Aruch and the poskim did not mean it literally that one should drink ad dlo yada bein… its just almost impossible. I drank an amount of wine that would knock most people under the table and all I got was really tipsy but if I made a little effort it was still very clear who was who. I realized that if I kept drinking I would just get nauseous and throw up and for most people that is the case, they would throw up well before ever getting drunk enough to really confuse the two. In fact I dont believe anyone who knows the story well and learned into it will be able to mix up Mordechai and Haman.
IMHO, the way I understood ad lo yada is to drink to the point where one can’t make Gematria calculations; i.e., forgetting the numerical values of the otiot.
BTW. The Gematria of “Baruch Mordechai” = The Gematria of “Arrur Haman” = 502
The chochmas manoch and yaabetz (amongst others) says that there was a piyut they use to say that started off arur haman baruch mordechai and went all the way until taf – and the gemarah meant if u couldnt get through the whole piyut you were drunk enough.
Perhaps it means that you can’t get the words right when you sing? Not that you don’t actually don’t know the difference, but you’re not coherent enough and jumble your words/lyrics, whatever they may be. You don’t have to davka make this mistake, but you’re drunk enough that such confusion is possible.