You can read the hebrew version here. Keep in mind that Rabbi Hirsch wrote the original letter in Hebrew and as far as I know there is no German translation of that.
Everything from here and below is just lihagdil Torah viyadir.
You should be able to find the Hebrew version that professor Mordechai Breuer submitted for the Teves installment of Hamayan 5736.
According to the footnote in Hirsch's collected writings volume 9 page 201, that is what they based their version off of.
And when I say you should be able to, I mean I can't verify that, as HebrewBooks doesn't seem to have that particular volume. (Why? Who knows maybe they censored it because there is a fringe opinion that Rabbi Hirsch didn't write that piece. Who knows.)
The article and snippets you see online are almost certainly from Rabbi Yehoshua Leiman's translation of the original letters. They were published in his Light magazine.
If you've found that translation wanting, perhaps give the version in the collected writings a try.
Also, the aforementioned footnote mentions that the originals belong to a collection of Hirsch letters purchased by Bar-Ilan University, so try your luck with them.