Using nonstandard gender-neutral pronouns to refer to myself in academic writing
It's your decision what to write, but to my mind, adding a note trying to explain your preferred pronouns seems like it puts the emphasis on something which you probably don't want to make the focus.
I'm young enough to be fairly familiar with this stuff, but I have to be honest, the thing I'd remember after read your paper would be "Huh, I've never seen anyone write a note like that before." I don't want to suggest the way you identify is something you want to hide, but remember that your article is going to be read (hopefully) by a lot of older people or people from other cultures who have no idea what "ze" is supposed to mean, and I assume your main goal is not to educate them about that stuff.
I would encourage you to instead use "they" or "we" when referring you yourself ("the PI presented on their research" or "we presented on our research"); these might be a little awkward, but they have an established pedigree in writing, and shouldn't strike people as too out of place.
Let me add two cents from the perspective of non-native speaker. Your inquiry was - in my case - the first time ever that I have heard of English gender-neutral pronouns. I think I may be not the only exception and therefore your paper may become harder to understand by a broader audience. Secondly, as noted by others already, usage of those pronouns is a non-standard practice (at least in my discipline), therefore it may overshadow other qualities of your work.
However, if you wish to not stress your gender, a number of stylistic figures may be employed. I can immediatelly think of two; firstly, as others have suggested, you may resort to using pluralis modestiae (i.e. we have discovered); secondly - why not try using passive voice (the PI's research was also presented at a local event to rephrase your example).
My advice is to use "they/their", or none at all.
You are suggesting to use a pronoun that the general public neither understands nor accepts, and could detract from your writing. If your subject was about such concepts of sexuality and identity, then it would be most appropriate to use. But for anything else, people aren't going to know what they mean, and will be annoyed at having to look it up. In fact, it will likely be seen as a type-o before it is looked up, and then, you would likely be imagined to be the sexuality identity of the reader. And a perceived type-o lessens the credibility of the author. All of this is an unnecessary distraction.
People use gender descriptions in order to try to portray an image of the subject. Issues of transgender are more of what is going inside the mind, and less about the physical appearances, and so, using adjectives and pronouns about transgender terms will not help to build that image the writer is trying to build. Of course, using neutral-gender words will force the user to imagine a subject of a gender they will have to imagine, as I said most likely their own gender. If you are concerned about what people might imagine the gender to be, as it might change what you are trying to convey, then by all means, use gender specific words - but using terms that have not been accepted by the public will only serve to create confusion.
In your example, you can even get away with removing pronouns altogether, or using "it" in 3rd person:
- "...the PI also presented on her research at a local event..."
- "...the PI also presented on its research at a local event..."
- "...the PI also presented on their research at a local event..."
- "...the PI also presented on research at a local event..."
or even:
- "...the local event will feature research done by the PI..."
But to the common reader:
"...the PI also presented on hir research at a local event..."
This is liable to be seen as meaning "her" instead of "hir", and using "ze" will be read like this:
"...the PI also presented on ze research at a local event..."
And here the reader is thinking you're trying to be cute with Germanesque idioms, unless I am also not using the term properly for the example. Nevertheless, new transgender terms are not uniform, as the community argues that some don't like some phrases because of the sound that implies gender. (eg, "sie" is German, sounds feminine, and means "hers" in German). Of course, only a German speaker would know this, but the fight continues.
Until the public understands these phrases, and when there is unity in the transgender community about which to use, your work is the last place to fight that battle, unless your work is itself about that battle.