Continuing on from my post yesterday, I wonder if going back to Old/Middle English could actually provide an answer? That had "hit" as a gender-neutral pronoun. Essentially "it" with an "h" in front. The "h" could serve as the bridge to "he" and "she", and people are already familiar with how "it" works in the language.
Yes, there already is the word "hit" in the language, but there are many homonyms and homographs in the language already, and context should work for this to alleviate any ambiguity.
So you could have:
Hit is eating an apple.
The apple is hits.
The apple belongs to hit.
I gave hit an apple.
Then again, I suppose some British accents could see that just becoming "it" again, which runs into the same problems as before. I could see maybe a different letter to make something like "dit", but then that runs into the problem of again being disconnected from "he" and "she". You obviously can't stick an s in front of the h.
I'll say it again, I don't think there's an easy solution, but I do think that there should be a better solution than the one that's currently taking hold.
I don't think that "hit" would ever gain much traction. For multiple reasons, not there least of them is can you imagine the likely outcomes if a school kid told the class to refer to them as "hit?" But I definitely think there is a fair about of difficulty in writing and saying "they," for a singular person and conveying what is meant by it, and hope that a better term will need chosen.
There is enough pressure from being non binary that ideally more time could be devoted around the identity of being non binary rather than discussing the confusing contradictory grammer surrounding it. Hopefully enough people will choose a better term for non binary pronouns, and there will be enough pressure for better terminology.
I remember when I first heard someone talk about someone else as a singular person with a multiple person pronoun, and I thought they were trying to gently imply that the person had schizophrenic multiple personalities.
Me: how are you doing, how has your family been?
Friend: great, my daughter got in to [some great college], and they are going there in the fall.
Me: that is great, you must be very proud. You said they, did you have multiple children going to the same college? That is great that they can be together.
Friend: no just my daughter.
Me: ummm, I apologize you said your daughter, but you referred to them as multiple people.
Friend: oh, they just identify as they.
Me: (I am not sure if his daughter has multiple personalities, and they have just started calling her "they" since they might not be sure which personality that they would be dealing with)
Me: ahh OK, well you must be very proud of them.
I mean with all of the work to get people to acknowledge non binary people, it is unlikely that the appropriation of "they" as a singular pronoun instead of plural will be replaced by something that makes more functional and grammatical sense. It will always continue to be a challenge since the use goes against basic grammer and logic, but there has been so much work to get enough people to accept it that it would be difficult to change to a term that is better defined and easier to use. There will definitely be a lot of continuous confusion for a long time because of it though.
I am sure they will people who will not accept the use of the plural pronoun "they" to refer to a singular person, not because they don't support someone being non binary, but because it logically does not make sense. The biggest problem with that is that the less people that use the preferred pronouns, the harder it will be for non binary people to gain normal social acceptance. Since the grammar contradictions around the chosen phrase of "they" as both a singular and plural pronoun are so difficult, those that chose that terminology made it much harder for non binary people as a whole.
Ideally, I would have preferred the pronouns "Ne" and "Nim" as short for neutral or gender neutral.