"such" can be used at the beginning and cause inversion only when it is an independent intensifier, that is, when it can be used alone.
Hello, Coco and Gustavo,
I agree with you, Gustavo, that (3) is the only decent sentence of the three and that "such" causes inversion when it appears as an independent intensifier at the beginning of a clause. I think there are rare cases, however, in which "such" is part of a larger noun phrase at the beginning of a clause in which subject-auxiliary inversion is used. Coincidentally, I just happened upon an example of this in Ethan Frome, a 1911 novella by Edith Wharton which I recently read and am now rereading:
"So marked was the change in her manner, such depths of sad initiation did it imply, that, with some doubts as to my delicacy, I put the case anew to my village oracle, Harmon Gow; but got for my pains only an uncomprehending grunt."
- Edith Wharton (bold lettering mine)
I think that perhaps, if Coco really wants to have the sentence begin with, as she puts it, "such + a noun" (i.e. a noun phrase of which "such" is a part), she could do so by changing "it" to expletive "there," making "public opinion" a noncount noun, and changing "strong" to "negative":
4. Such negative public opinion was there that he had to resign.