What Is The Meaning Of The "True Religion"?

In six places in the Yad Hachazaka, the Rambam uses the term דת האמת - "the true religion" - and here they are:

One must begin [the narrative describing our ancestors'] base [roots] and conclude with [their] praise. What does this imply? One begins relating how originally, in the age of Terach, our ancestors denied [God's existence] and strayed after vanity, pursuing idol worship. One concludes with the true faith - דת האמת: how the Omnipresent has drawn us close to Him, separated us from the gentiles, and drawn us near to His Oneness. [Chometz U'matza 7/4]

We are obligated to be careful with regard to the mitzvah of charity to a greater extent than all [other] positive commandments, because charity is an identifying mark for a righteous person, a descendant of Abraham, our patriarch, as [Genesis 18:19] states: "I have known him, because he commands his children... to perform charity." The throne of Israel will not be established, nor will the true faith ודת האמת stand except through charity, as [Isaiah 54:14] states: "You shall be established through righteousness." And Israel will be redeemed solely through charity, as [ibid. 1:27] states: "Zion will be redeemed through judgment and those who return to her through charity." [Matnos Aniyim 10/1]

It is a positive commandment to gather together the entire Jewish people - men, women, and children - after every Sabbatical year when they ascend for the pilgrimage holiday and to read so that they hear passages from the Torah that encourage them to perfom mitzvot and strengthem them in the true faith - בדת האמת, as Deuteronomy 31:10-12 states: "At the end of a seven-year period, at the time of the Sabbatial year on the Sukkot holiday when all Israel come to appear... gather the nation, the men, the women, the children, and your stranger in your gates...." [Chagiga 3/1]

Converts who do not understand are obligated to concentrate their attention and direct their hearing, listening with reverence and awe, rejoicing while trembling as on the day the Torah was given at Sinai. Even great Sages who know the entire Torah are obligated to listen with exceedingly great concentration. One who is unable to hear should focus his attention on this reading, for Scripture established it solely to strengthen the true faith - דת האמת. He should see himself as if he was just now commanded regarding the Torah and heard it from the Almighty. For the king is an agent to make known the word of God. [Chagiga 3/6]

All the lands that he conquers belong to him. He may apportion them to his servants and soldiers as he desires and keep the remainder for himself. In all these matters, the judgement he makes is binding.
In all matters, his deeds shall be for the sake of heaven. His purpose and intent shall be to elevate the true faith - דת האמת and fill the world with justice, destroying the power of the wicked and waging the wars of God. For the entire purpose of appointing a king is to execute justice and wage wars as I Samuel 8:20 states: 'Our king shall judge us, go out before us, and wage our wars.' [Melachim 4/10]

Do not presume that in the Messianic age any facet of the world's nature will change or there will be innovations in the work of creation. Rather, the world will continue according to its pattern.
Although Isaiah 11:6 states: 'The wolf will dwell with the lamb, the leopard will lie down with the young goat,' these words are a metaphor and a parable. The interpretation of the prophecy is as follows: Israel will dwell securely together with the wicked gentiles who are likened to a wolf and a leopard, as in the prophecy Jeremiah 5:6: 'A wolf from the wilderness shall spoil them and a leopard will stalk their cities.' They will all return to the true faith - לדת האמת and no longer steal or destroy. Rather, they will eat permitted food at peace with Israel as Isaiah 11:7 states: 'The lion will eat straw like an ox.'
Similarly, other Messianic prophecies of this nature are metaphors. In the Messianic era, everyone will realize which matters were implied by these metaphors and which allusions they contained. [Melachim 12/1]

Apparently, דת האמת means Yiddishkeit - Judaism. However, the last Rambam we quoted seems to refute that theory. The Rambam says that when Moshiach comes the goyim will return to the true faith and no longer steal and destroy. Does this mean that they will convert? Not stealing and destroying [killing] are included in the sheva mitzvos bnei noach, so it doesn't seem to mean that the goyim will convert. [The Rambam implies in Hilchos Teshuva 9/2 and Melachim 12/4 that when Moshiach comes the goyim will remain goyim and not convert]. So maybe when he says that they will return to the "true religion", he means to the sheva mitzvos bnei noach [that they must keep because it is part of the Torah [Melachim 8/10-11].

The question is what he means in the other places. In the Kovetz Hayaros Hatmimim [Manchester 5767] an article suggests that in all places the Rambam means the same thing. דת אמת connotes a more broad true faith in G-d together with his Torah and sheva mitzvos beni noach and not a more narrow true faith in Yiddishkeit.

I am not convinced.... The first four Rambam's [and maybe 5] I quoted can mean Toras Yisrael in the more narrow sense and not refer to a general faith in G-d and his moral law of sheva mitzvos. The first Rambam certainly would seems to have a more parochial Jewish meaning [.... One concludes with the true faith - דת האמת: how the Omnipresent has drawn us close to Him, separated us from the gentiles, and drawn us near to His Oneness] and so the mitzva of Hakhel [Rambam 3 and 4] is for Jews alone.