Questions for the Lore Masters.

The Dwarves add that at that time Aule gained them also this priviledge that distinguished them from Elves and Men: that the spirit of each of the Fathers (such as Durin) should, at the end of the long span of life allotted to Dwarves, fall asleep, but then lie in a tomb of his own body, (note24) at rest, and there its weariness and any hurts that had befallen it should be amended. Then after long years he should arise and take up his kingship again.

JRRT, The Peoples of Middle-Earth

"Actually the matter of the elvish tongue of the "Silvan folk" is rather confused in the L. R."

JRRT, Words Phrases And Passages (written between the first edition and the second, revised edition).

UT, Galadriel and Celeborn wrote:Amroth was King of Lórien, after his father Amdír was slain in the Battle of Dagorlad [in the year 3434 of the Second Age]. His land had peace for many years after the defeat of Sauron. Though Sindarin in descent he lived after the manner of the Silvan Elves and housed in the tall trees of a great green mound, ever after called Cerin Amroth. This he did because of his love for Nimrodel. For long years he had loved her, and taken no wife, since she would not wed with him. She loved him indeed, for he was beautiful even for one of the Eldar, and valiant and wise; but she was of the Silvan Elves, and regretted the incoming of the Elves from the West, who (as she said) brought wars and destroyed the peace of old. She would speak only the Silvan tongue, even after it had fallen into disuse among the folk of Lórien; and she dwelt alone beside the falls of the river Nimrodel to which she gave her name.

UT, Galadriel and Celeborn wrote:Although the dialects of the Silvan Elves, when they again met their long separated kindred, had so far diverged from Sindarin as to be hardly intelligible, little study was needed to reveal their kinship as Eldarin tongues. Though the comparison of the Silvan dialects with their own speech greatly interested the loremasters, especially those of Noldorin origin, little is now known of the Silvan Elvish. The Silvan Elves had invented no forms of writing, and those who learned this art from the Sindar wrote in Sindarin as well as they could. By the end of the Third Age the Silvan tongues had probably ceased to be spoken in the two regions that had importance at the time of the War of the Ring: Lórien and the realm of Thranduil in northern Mirkwood. All that survived of them in the records was a few words and several names of persons and places.

LOTR, Appendix F wrote:The Elves far back in the Elder Days became divided into two main branches: the West-elves (the Eldar), and the East-elves. Of the latter kind were most of the Elven-folk of Mirkwood and Lorien; but their languages do not appear in this history, in which all the Elvish names and words are of Eldarin form.

In Lórien at this period Sindarin was spoken, though with an 'accent', since most of its folk were of Silvan origin. This 'accent' and his own limited acquaintance with Sindarin misled Frodo (as is pointed out in The Thain's Book by a commentator of Gondor). All the Elvish words cited in Book Two chs 6, 7, 8 [the Lórien chapters of FOTR] are in fact Sindarin, and so are most of the names of places and persons. But Lórien, Caras Galadhon, Amroth, Nimrodel are probably of Silvan origin, adapted to Sindarin.

"... for there were other Elves of various kind in the world; and many were Eastern Elves that had hearkened to no summons to the sea, but being content with Middle-earth remained there (...) Of that kind were the Elves of Greenwood the Great; yet among them also were many lords of Sindarin race. Such were Thranduil and Legolas his son. In his realm and in Lorien both the Sindarin and the woodland tongues were heard; but of the latter nothing appears in this book, and of the many Elvish names of persons or of places that are used most are of Grey-elven form."

Eldorion wrote:Something else that occurred to me while I was doing some unrelated Tolkien reading were the following comments regarding King Tarannon Falastur of Gondor, who reigned T.A. 830-913, although his military accomplishments came before he ascended the throne.

LOTR, Appendix A.I.v wrote:With Tarannon, the twelfth king, began the line of the Ship-kings, who built navies and extended the sway of Gondor along the coasts west and south of Mouths of Anduin. To commemorate his victories as Captaiin of the Hosts, Tarannon took the crown in the name of Falastur 'Lord of the Coasts'.

At this point, a map of Gondor's coastlines along the Bay of Belfalas might be useful. I'll use this one from the Encyclopedia of Arda:



Falastur's successors mainly pushed his conquests further south, subjugating Umbar, the surrounding region, and eventually all of Harad as tributaries. Therefore, Falastur is mainly noted for his conquest of Harondor (South Gondor), since that set the stage for the subsequent conquests, which helped launch the golden age of Gondor in the Third Age. However, what I'm more interested in is the comment that Falastur pushed the borders of Gondor west, into regions with no clear geographical division from the core area of Gondor, but that is implied to have put up armed resistance to Dúnedain conquest. These are the same regions inhabited by the pre-Dúnedain indigenous inhabitants of Gondor discussed in the OP.

Now, the area immediately to the west of the Mouths of Anduin (aka Ethir Anduin; a river delta) are southern Lebennin, then followed by Dor-en-Ernil and/or Belfalas (depending on whether you consider those two terms to be synonyms or not). I believe that these regions, especially Lebennin, would have been firmly integrated into the realm of Gondor before Falastur's time. In Unfinished Tales it is stated that Isildur took his nephew Meneldil and journeyed around the borders of turn-of-the-Age Gondor, before finally creating a burial mound for Elendil on the hill Eilenaer (later Amon Anwar) because it was "near to the center of the lands of Gondor" and was later considered the official "mid-point of the Kingdom of the South" (as opposed to Arnor, the Exilic Kingdom of the North; UT, Cirion and Eorl, The Tradition of Isildur).

Just judging by eye from the official maps, Amon Anwar appears to have been nearer to the southern frontier of Gondor in its original borders, but fairly close to the middle, prior to the cession of Calenardhon to the Rohirrim. UT notes, it was that cession that prompted the removal of Elendil's tomb to Minas Tirith on the grounds that Amon Anwar was no longer the center of the realm, since Gondor had voluntarily given up the lands that would become Rohan, as opposed to losing them in war. Interestingly, "The Tradition of Isildur" makes no note of the vast lands that Gondor had gained (and in some cases subsequently lost) during the Third Age. It appears that those were not factored in, implying either that they were always considered mere territories or, in my opinion the more likely option, that it was really just the fact that they didn't want Elendil's tomb to be on the border with a foreign country (as is noted in UT) that prompted the move, moreso than any preoccupation with geometry that might have been given as an excuse.

Anyway, what is more relevant to the OP is that Amon Anwar is also pretty damn close to the mid-way point between Minas Tirith and Dol Amroth on the east-west axis, although it is farther north than either of them. This suggests to me that the Second Age boundaries of Gondor did not extend much further west than Dol Amroth south of the White Mountains. (North of the Mountains is a different matter, as we know the early Gondorians constructed Helm's Deep and Isengard considerably further west, though that would make Amon Anwar not so central.) This would put the Princes of Belfalas (since Dol Amroth had not yet acquired that name) right on the frontier of Gondor, I think lending further circumstantial evidence to my case regarding the nature of their princedom and the greater use of Adûnaic.

One final note, the fact that Falastur is noted as a conquerer of coastal regions makes it pretty clear that the Anfalas (roughly the Gondorian coast to the west of Edhellond) was still inhabited by native Gondorians eight centuries into the Third Age. This makes it pretty much indisputable that the arrival of Elves in Edhellond did not result in the wholesale removal of the native population from the entire coast. I suppose it remains a somewhat open question regarding when the native inhabitants were displaced in the areas east of Edhellond, nearer to the Anduin, but given that all of our late Second Age/early Third Age references are about them as men of the mountains, I think it's safe to say that, at the latest, the arrival of the Númenóreans in the Anduin valley prompted their removal. Again establishing the unique position of Dol Amroth as a major coastal settlement that nonetheless had to deal with close non-Dúnedain neighbors for nearly a millennium after the establishment of Gondor.