Berachot 15a: What does Rabbi Yossi derive from 'Shema'?

Consider the following Mishna and Gemara on daf 15a:

מתני' הקורא את שמע ולא השמיע לאזנו יצא ר' יוסי אומר לא יצא קרא ולא דקדק באותיותיה ר' יוסי אומר יצא רבי יהודה אומר לא יצא הקורא למפרע לא יצא קרא וטעה יחזור למקום שטעה:

גמ' מאי טעמא דר' יוסי משום דכתיב שמע השמע לאזנך מה שאתה מוציא מפיך ות"ק סבר שמע בכל לשון שאתה שומע ור' יוסי תרתי שמע מינה .

Or, in English:

MISHNAH. IF ONE RECITES THE SHEMA' WITHOUT HEARING WHAT HE SAYS, HE HAS PERFORMED HIS OBLIGATION. R. JOSE SAYS: HE HAS NOT PERFORMED HIS OBLIGATION. IF HE RECITES IT WITHOUT PRONOUNCING THE LETTERS CORRECTLY, R. JOSE SAYS THAT HE HAS PERFORMED HIS OBLIGATION, R. JUDAH SAYS THAT HE HAS NOT PERFORMED HIS OBLIGATION. IF HE RECITES IT BACKWARD,⁵  HE HAS NOT PERFORMED HIS OBLIGATION. IF HE RECITES IT AND MAKES A MISTAKE HE GOES BACK TO THE PLACE WHERE HE MADE THE MISTAKE.

GEMARA. What is R. Jose's reason? — Because it is written, 'Hear' which implies, let your ear hear what you utter with your mouth. The first Tanna, however, maintains that 'hear' means, in any language that you understand. But R. Jose derives both lessons from the word.

This conclusion by the setama degemara, that Rabbi Yossi derives two lessons from a single word, seems quite uncharacteristic, to say the least. Personally, I think that indeed this is possible, and it is a frustrating and ultimately mistaken exercise to attempt to create a consistent system of derasha in which each word or word-part of a pasuk is mapped to precisely one halacha, and vice versa. But if we do attempt this, then here is how one can resolve Rabbi Yossi, without this dual derasha from a single word.

See the parallel Yerushalmi Berachot 16a-b, where his derasha turned out to be from a different pasuk:

א"ר יוסי הוינן סברין מימר מה פליגין רבנן ורבי יוסי בשמע דכתיב בה שמע הא שאר כל המצות לא.  מן דמר רב מתנה דר' יוסי הוי היא שאר כל המצות.  מ"ט דר' יוסי (שמות טו) והאזנת למצותיו ישמעו אזניך מה שפיך מדבר.  

(The first Rabbi Yossi in this Yerushalmi is the Amora, while the second and third mention are of the Tanna.) Of course, one could still assert that the primary derivation was from the word שמע and the extension to all mitzvot was from this other pasuk.

Meanwhile, in our own Bavli, the running assumption is that Rabbi Yossi would hold that the requirement for words to reach one's ears apply across all mitzvos, including terumah, birkat hamazon, megillah.

And Rav Yosef (thus, another Rabbi Yossi), before being rewritten by the setama, that is, in the hava amina, asserts that all agree, not just Rav Yosef, that all other mitzvos require being audible:

R. Joseph said: The difference of opinion relates only to the recital of the Shema', but in the case of other religious acts all agree that he has not performed his obligation [if he says the formula inaudibly], as it is written, attend and hear, O Israel.⁶  An objection was raised: A man should not say grace after meals mentally, but if he does he has performed his obligation! — Rather, if this statement was made it was as follows: R. Joseph said: The difference of opinion relates only to the Shema', since it is written, 'Hear O Israel'; but in regard to all the other religious acts, all are agreed that he performs his obligation. But it is written, 'Attend and hear, O Israel'? — That [text] applies only to words of Torah.⁷

The reference is to a completely separate pasuk, in Devarim 27:9:

ט  וַיְדַבֵּר מֹשֶׁה וְהַכֹּהֲנִים הַלְוִיִּם, אֶל כָּל-יִשְׂרָאֵל לֵאמֹר:  הַסְכֵּת וּשְׁמַע, יִשְׂרָאֵל, הַיּוֹם הַזֶּה נִהְיֵיתָ לְעָם, לַה' אֱלֹהֶיךָ.

9 And Moses and the priests the Levites spoke unto all Israel, saying: 'Keep silence, and hear, O Israel; this day thou art become a people unto the LORD thy God.

The hava amina is difficult to understand, even if we put aside the brayta. Why should Shema be less stringent than the other mitzvos, especially if we don't have any exclusionary derasha.

At any rate, this statement by Rav Yosef would account for why our gemara can't give this extra pasuk as a basis for Rabbi Yossi. Rav Yosef of Bavli is like the initial assumption of Rabbi Yossi the Amora in Yerushalmi.