The most complete example of נוסח פרס that is available, JTS Adler ENA 23, was reproduced by Shlomo Tal to which he added his commentary. The book can be viewed at hebrewbooks.org/20923.
I would like to introduce the Nusach by highlighting several Piyuttim that are found within it. The first is an extended version of a Piyut that is already found in all Siddurim as part of the first Bracha of Kriyat Shema. However, in those Siddurim the alphabetical acrostic ends at the letter Gimel.
The second Piyut is found at the end of Shemona Esrei:
I was able to trace the source for the line that concludes Shemona Esrei:
מדרש תהלים (שוחר טוב; בובר) מזמור יט-יהוה צורי וגואלי. צורי בים סוף, וגואלי בעמלק. צורי במרה, וגואלי בסיני. צורי בעולם הזה, וגואלי בעולם הבא.
A third Piyut is found within their version of ברוך שאמר for Shabbat. I am attaching a transcribed version of it:
My purpose in presenting excerpts from the extinct נוסחי התפילה
is that they should not be forgotten, particularly since studying them enhances our Tefila experience.
What caused these prayer rites to become extinct? In the case of מנהג צרפת, the French Ashkenaz rite, it was the expulsion of the Jews from France in 1394 and their inability to come together as a group in any one place to be able to continue their Nusach. That was the opposite case with the Jews who were expelled from the Iberian Peninsula beginning in 1492. They arrived at some places in such great number that they caused communities to abandon their local Nusach Ha'Tefillah and to accept the Nusach of the new arrivals. In addition, the Rabbis who were among those expelled were highly respected and based on their customs, the communities accepted the Rabbis' Nusach Ha'Tefillah. That was the case for Nusach Romania and Nusach Aram Tzova. Concerning the Persian Rite, it was still followed in Bucharia as late as the 1700's. However, with the arrival of a well-respected Rabbi, the community was persuaded to change their Nusach Ha'Tefillah from the Persian Rite to the Sephardic one.
In more recent times, it was the extermination of Jews by the Nazis that decimated communities with distinct Nuscha'Ot. Not enough of their followers remained and returned to their communities to resume their rites. That was the case for Nusach Corfu and Nusach Carpentras.
Thankfully digitized examples of these Nusach'Ot are available particularly through the Ktiv Hebrew Manuscript website and the Book Repository of the National Library of Israel.