This is a question into which I have done a little bit of research.
There are two independent issues:
- Saying ה שפתי תפתח before the עמידה
- Taking three steps forward or back or both, which is an issue in itself
Saying ה שפתי תפתח is attributed to R. Yohanan in Brakhot 4b
והא אמר רבי יוחנן בתחלה אומר ה' שפתי תפתח ולבסוף הוא אומר יהיו לרצון אמרי פי
and the statement is a little clearer in the Yerushalmi Berakhot 8a:
רבי יוסי ציידניא בשם רבי יוחנן לפני תפילתו הוא או' ה' שפתי תפתח ופי יגיד תהילתך לאחר תפילתו הוא אומר יהיו לרצון אמרי פי והגיון לבי לפניך ה' צורי וגואלי
Taking three steps is more complicated:
Yoma 53b has the following statement:
אמר רבי אלכסנדרי אמר רבי יהושע בן לוי: המתפלל צריך שיפסיע שלש פסיעות לאחוריו, ואחר כך יתן שלום
There is no indication of when these steps are taken, or what exactly ואחר כך יתן שלום means. But it seems clear from the context that this is referring to the end of the Amidah. So we have a source in the Talmud for taking three steps backwards at the end of the Amidah, but nothing about three steps forward, nor anything about the beginning of the Amidah.
Rashi in his siddur mentions that we take three steps forward before the Amidah, and three steps backwards. These three steps forward at the beginning of the Amidah appear to have developed as a "mirror image" of the three steps backwards at the conclusion.
Mishnah Berurah OH 95:3 writes:
ילך לפניו - ואין צריך לחזור לאחוריו כדי לילך לפניו כ"כ הא"ר אבל מנהג העולם לילך לאחוריו
which seems to imply that the reason we take three steps backwards is essentially to have space to take the three steps forward, but it's the three steps forward that actually "count" - those are the steps with which we symbolically step into the presence of the רבונו של עולם
Finally, regarding the steps at the END of the Amidah, the Magen Avraham writes (OH 123:2):
ואחר שפסע - לא כאותן שאומרים עושה שלום בעוד שפוסעין דאין נכון לעשות כן
The Magen Avraham disagrees with those who take their three steps backwards at the conclusion of the Amidah WHILE saying the words עושה שלום במרומיו. Although he does not state so explicitly, one could assume that he would also disagree with the practice of taking three steps backwards and forwards - one word per step - when saying ה שפתי תפתח at the beginning of the Amidah.
Now, to finally try to answer your question; you asked which opinion is "authoritative":
I don't believe that there is an authoritative answer to this question because it is a matter of custom. Though some may disagree with me on that, as my example in a moment will show.
I started out writing that I have done some research on this topic, which has included polling several hundred people about their own personal practice. Because this is a practice that people do silently and on their own, we don't usually notice what other people do. Furthermore, I think it is the sort of custom that we are unlikely to change from the way that we learn to do it when we first learn to say the Amidah, because in the absence of seeing others do it differently, we have no reason to change our practice. Consequently, I think that my polling method accurately reflects what people learned about taking steps when they first learn (usually as children) to say the Amidah.
My polling has shown that slightly over half of the people I've polled practice (B) of your choices above, that is, they take their three steps backwards and three steps forward while saying the six words of ה שפתי תפתח ופי יגיד תהלתיך - one word per step.
What is really interesting though is the other half. Most of them take their steps back and forward at some point prior to saying ה שפתי תפתח. BUT, a significant majority of them originally learned to do one step per word (option B), and later changed their practice either because of the instructions in the ArtScroll Siddur or because a Rabbi told them to change their practice.
I should also point out that for the most part my poll has been limited to the Ashkenazic modern-Orthodox community. It would be interesting to poll Sefardic, yeshivish and chassidish, etc. communities as well.
It seems to me then (and this is ongoing research that I hope to continue with harder data), that the overwhelming practice is to take one step per word.
As I said, this does not help with an "authoritative" answer.
