I wanted to update for anyone who might be curious:
The entire process was *extremely* straightforward, with the exception of getting the notice of publication waived. When you submit your request for a change of name to the prothonotary, you HAVE to simultaneously submit a petition to waive the publication.
The only catch? There is no form to waive the publication. I'm talking I sat in The Law Library and dug for hours with a bunch of knowledgeable people and it isn't there. So you have to write your own. So it looks legal-ish.
What I ended up doing was printing a form called "praecipe for determination," and filled it out with my reasons for not wanting to publish the name change (violence against transgender people, etc.). Then on the form where it says "praecipe for determination," the prothonotary told me to white that out and simply write, "petition to waive publication."
I submitted it all. The judge received my request that day, and I received the letter in the mail today that my requirement to publish an article was officially waived.
I was ABSOLUTELY STUMPED about what to do because I had no idea how to write up a petition in legalese, so thank god the librarian helped me find a form to use as a template for what I needed.
For anyone else in my county: the librarian also permanently added that form to the database, because apparently lots of trans people come through and get stumped at this step, so now it's on the computer with all the other name change forms.