I'm very happy to report that in a unilateral decision, Sarada has chosen to refer to me using a gender-neutral pronoun. Clearly it is very difficult for her to refer to me as "she" and needless to say that is my preferred pronoun, but one thing I would prefer even more is to be in a culture without gendered third person pronouns. so this is a way of harnessing my linguistic nerdiness to a common end.
In fact, the English language already has lots of gender-neutral pronouns, and in fact Sarada already refers to me using one of those, namely "you". This wouldn't be possible in all languages by any means, for instance Arabic uses "anti" and "anta" for singular "you" depending on the gender of the addressee. As I think I mentioned before, I personally consider the word "I" to be gendered for myself because before transition was thrust upon me I used a lower case "i", so in my idiolect, "I" is feminine and "i" masculine, since I now feel OK about myself to a considerably greater degree and am at peace with the anomalous and unique English narcissism of using a capital letter for it. That doesn't mean, incidentally, that I think anyone else should or should not do that. This distinction is also inaudible.
Regarding the third person, Sarada and I differ in our ideas about referring to people as "it". I would prefer "it" to "he" regarding myself, as it feels less insulting, although it probably is a little insulting, just not so much as "he" is, which feels worse than being called "b****" or the C-word, but, oddly, slightly better than being called "sir". That doesn't mean I think people calling me that are actively trying to upset me. There is also a precedent for using "it" to refer to people, particularly children. Human feti and embryos are often called "it", which when you think about it is a bit weird because at least in the first trimester they are all arguably female. Generally though, using "it" even to refer to children nowadays seems to be frowned upon, so fair enough.
One really elaborate way round this would be to start using a language without gendered pronouns, such as my favourite language, Finnish, which when it uses subject pronouns at all will generally use "se" for the singular and "ne" for the plural, but has "hän" for the singular, rather like the Scandinavian languages. However, the learning curve for the God Language is so steep that in spite of spending more than three decades trying to pick it up I'm still only a beginner, so the chances of Sarada and I wishing each other hyvää aamu or ordering a cup of kahve in it are small. A somewhat easier option would be the most widely spoken language in Iran, which just uses "u" for she, it and he, I think partly because the rest of its culture is so gendered that nobody feels the need to express it in pronouns. Malay/Indonesian also has gender-neutral third person singular pronouns.
"This", "that" and "they" are all gender-neutral. I wouldn't mind being called "this" or "that" at all, although it would probably sound a bit odd. "They" is a viable pronoun to use in the singular in my opinion, rather along the lines of how we use "you" for "thou" mostly even though that can be very confusing.
For a short period in the Middle Ages, I seem to recall that some dialects of English lacked gender distinction between feminine and masculine. It was something like "a" or "ha" in the nominative, i.e. the case in which "she" is. "She" and "he" also fell together at some point as Old English had used "heo" and "he", but that rather unhelpfully led to both of them becoming "he".
Malay/Indonesian has what is known as the T-V distinction in all pronouns, i.e. polite and informal versions. Just as we might say "you" until we know someone well enough to call them "thou", and if you think about it that still works because saying "thou" to a stranger is likely to get them looking funny at you because they aren't yet used to how much of a weirda you are yet and don't realise you're going to do something like that, Malay/Indonesian has that for many pronouns. If you want to show respect, you call yourself "saya", which originally meant "the slave", but once you get to know someone with whom you are on equal terms, you can start calling yourself "aku". This applies to the third person too, where the polite form is "beliau" and the informal "dia". That language is in fact, as Anthony Burgess, fellow language nerd, "bafflingly easy", so maybe we should just all speak it, and I mean all of us, not just us two. There's another gap in the pronominal inventory of our speech - the word "wit"/"unc" has fallen into disuse so we have to write "us two" instead.
It seems to me that if Sarada were to start using a gender-neutral third person pronoun for me, it would automatically be a familiar or informal one like "thou", because she knows me well. There are various suggestions for gender-neutral pronouns floating about, notably the Spivaks, but they tend to be very unsatisfactory. Spivak pronouns, for instance, just sound like you're dropping H's to me, and "em" is also almost identical to "'em". I quite like "thon", which is also the accusative (approximately "me", "thee", "us", "them" and "whom") form of "that", which was apparently suggested in Victorian times, and may also still exist in some dialects of English.
What Sarada et al seem to be batting around, though, is "mer". This presumably refers to my use of names with M in them. I've also been called "shim", which was creative, and was widely used by people I didn't know and is actually fine - the objective ending appeals to me. Sarada is going to do what she will, naturally, as is her right, but after some initial discomfort, I've decided "mer" would be OK although it's a bit third gendery. The reason I like it is that it sounds like the first syllable of "mermaid", "mersheep", "mergoat" (which Daniel - the Introstealer's real name - is as a Capricorn) "merman" and the like, and the metaphor of the mer-entity has been used to refer to trans people before because they're amphibious and occupy two environments. Whereas I'm not sure about that construction, I can get on board with the idea of occupying two worlds, even if one of them was largely against my will, because you have to try to salvage something positive out of your experience.
So "mer" would be OK although I might hold out for proper declension. In the end, it's up to her of course.