Just one caution for 自分: It’s used by everyone, but usually in contrastive context. As in, “my own,” or “specifically I, myself, did that (as opposed to someone else),” etc. There are people who use it as a general first-person pronoun, but it can seem a little pompous.
You can find some Japanese writing on struggling with pronoun choice as a non-binary or transgender person, but upon a quick lunch-hour search, I wasn’t able to find much on new pronoun-creation, and by and large Japanese speech skirts the need for it, as mentioned above. Doesn’t mean there aren’t cases or budding movements I’m not aware of.
In general though, you rarely have a need to invoke pronouns to refer to other people, unlike English, and for first-person pronouns, although there are gendered nuances, they’re also more gender-neutral than they first appear. 私 is neutral but slightly feminine leaning in private contexts, 僕 is male-leaning but actually used by cis women sometimes throughout Japan, to the point that it’s characterizing but not wildly unexpected, etc. The author of that article talks about mostly using 私, but making context calls. Even someone feminine-appearing using 俺, and even outside of the regions where it’s more standard–while it would call attention rather than avoiding it–isn’t going to shatter anyone’s worldview, and could be an option in informal contexts depending on the image you want. You can probably find something that feels right while remaining suitably neutral, though there might be emergent ones to fill in connotative niches too (ex. something as completely neutral as 私 that also doesn’t seem so distancing or slightly effeminate in personal contexts).
(Not an expert; just interesting and good to be aware of, so thanks for prompting a search. Will be interesting to see if anyone has more personal experience navigating these waters in Japan.)
@yndajas Thanks for reposting that link!