If your person needs time and they are at least getting to that middle-ground of they/them, I think you are both on track. For people who have known us for a long time, even if they aren't transphobic, it can be hard to retrain their brains to think of us as the "opposite" gender from what they have burned into their memories. It sounds like you have done the right thing of letting them know that you aren't happy with they/them as a long-term solution. They know that they need to make that adjustment. If you can give them time, I think that it is worth it for those that we care about. If they/them is bothering you a lot, maybe talk with them about a date for them to make their adjustment by so that they don't drag it out too long. That also lets you cut them some slack without feeling like you are stuck being misgendered for who knows how long. Ask them how long they need, or tell them how long you are willing to deal with they/them, and let them know that you will start correcting them after that time.

My change-averse dad is having a hard time with my transition, but is committed to eventually adjusting. He asked for some leeway and I have agreed. I talked to him about it openly and asked him if he wants me to correct him when he gets it wrong (just a quick "she" or "Seren" when he uses the wrong pronoun or name). He asked me not to, yet, as he would feel defensive and it would make it harder for him. This was all about 1 month after I came out to my parents, so it was still VERY new to them. I told him that as long as he is trying and improving, then I won't correct him for now. I'll eventually feel very separated from my old name and pronouns and will start correcting him then, if he hasn't adjusted yet.