I see your issue and I understand. Obviously I don't know what method you're using in coding for the different pronouns, but I'm just assuming you've done it so that it will opt in whichever option the player chooses rather than rewriting the entire script just with different pronouns. If you're doing it like that, you're right, just putting in they/them wouldn't work, you would have to make a different sentence structure. Using your example;
"No, they've got a point there."
I imagine that would require a lot of rewriting and fiddly coding and whatnot so I can completely see how that would just be too tasking, but I do appreciate that you at least looked into it, or even have a pronoun option at all.
If ever in the future you want try going for more pronoun options, the dating sim "Dial Town" would be a good example of an expansive pronoun option, it has standard options (He/She/They), but also has a completely customizable option, where the player can use anything as pronouns. You have to jump through some hoops because it means writing each pronoun for each context and whether it's plural etc etc, but I personally found it neat. (If you do look into it, the game is rather weird, but the pronoun thing is solid). I have no clue if the dev is using the same game engine as you, so I don't know if the code would even be transferable, so perhaps it would be useless to you.
I'd be happy to tell you about how they/them pronouns work, although not an expert (I'm also dyslexic, my ability at grammar may not be the most reliable) I just have some friends who use they/them and have thus had to adjust my language to accommodate that
Sorry for the essay and thank you for your original response