The canonical names Tolkien gave the family consisted of:

                 Silmarien = Elatan
                           |
                        Valandil
                           :
                           :
                +----------+----------+
                |                     |
             Earendur              Lindorie
                :                     |
                :                  Imzilbeth
                :
             Numendil
                |
         +------+-------+
         |              |
       Amandil       Elentir
          |
       Elendil
          |
          +----------------------------+
          |                            |
       Isildur                      Anarion
          |                            |
     +----+-+-------+------+           |
     |      |       |      |           |
  Elendur Aratan Ciryon Valandil    Meneldil

Now, of all these people, only Valandil was born in Middle-earth, but since his name was that of the first Lord of Andunie, I'm pretty sure we can regard his name as being a continuation of the family tradition.

I believe the Kings of Arnor and Gondor after Valandil and Meneldil established new traditions, so I would be reluctant to suggest their names were used in Andunie, except where they are obviously named for an ancestor.

One reasonable question is whether any Lord of Andunie would use the name of a King of Numenor. Anarion seems to have been named for Tar-Anarion, the eighth king, and Amandil seems to have been named for Tar-Amandil, the third king. Elendil bears the name of Tar-Elendil, the fourth king. So it's possible some of the earlier lords were named for kings as well, although I doubt they would have used the names of kings after Tar-Ciryatan.

On the other hand, if the Kings of Arnor and Gondor really moved away from using Andunien names, would they have done so immediately? I don't think so. So maybe Eldacar and Cemendur are "Numenorean" names (by that I mean they may have been commonly used by the family in Numenor), whereas later Quenyan names were either selected to commemorate Third Age events (such as Hyarmendacil) or to honor remote ancestors (such as Earendil) or heroes (such as Elendur, although he was only a few generations removed from Valandil, youngest brother of Elendur, Isildur's eldest son).

I'm pretty sure no Lord of Andunie would have presumed to take (or to bestow upon a son) any name beginning with "Tar-", which implied a kingship. So names like Tarcil and Tarondor and Tarannon are clearly not to be associated with the family history, and represent a departure from family naming conventions which descended from the Numenoreans. Hence, these "Tar-" and event-related names are strong evidence that the family eventually abandoned (for the most part) the older name set used in Numenor.

Third Age names I would regard as probable for Andunien family names would include: Eldacar, Valandur, Cemendur, Earendil, Earendur, and Anardil (the given or birth name of Tar-Aldarion). Possibly also Valacar, Aldamir, and Siriondil.

Of the first group, all are attested in early genealogies somewhere, or are close in form. Of the second group, they are close in form to names in the early genealogies.

With respect to your list, I suggest the following names are thus unlikely:

2. Eldacar (1035 - 1194) Too much of a foreshadowing of the Arnorian descent.

3. Silmarion (1194 - 1340) I don't believe this would have been used. Just a gut feeling.
7. Telumehtar (1700 - 1959) Doesn't seem to fit with the family naming conventions.
8. Vilyanúmen (1959 - 2119) Doesn't seem to fit with the family naming conventions.
10. Herendil (2256 - 2386) Includes the "her-" element implying lordship, even though the name could mean "Devoted to the lord" (or to one's lord).
12. Ciryaher (2518 - 2644) Includes the "her" element implying lordship.
14. Ulmondil (2775 - 2879) Doesn't seem to fit with the family naming conventions.

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