Well, it took almost 10 months, but I think I've stumbled upon some definitive information about the White Tree emblem.
The emblem of Elendil and his heirs was seven five-pointed stars, each representing one of the palantíri that Elendil brought from Númenor. (I've found no mention of the Stone of Erech, which was also brought back from Numenor during Numenor's Fall with the Flight of the Faithful.) In Gondor they (the seven stars) were set on a sable (black or off-black) coat of arms, together with the White Tree, which represented any of the descendants of the tree Nimloth that grew in Minas Ithil and later, Minas Tirith.
The Kings of the line of Elendil added the Silver Crown, which was the chief mark of royalty. This is not to be confused with the crown and seven stars used by Durin and his folk. Tolkien's own design for this crown was quite different, and he distinguishes the Dwarven use of the seven stars as not representing the palantiri, but the constellation of the Valacirca, or the Plough, which Durin saw above his head when he looked into the Kheled-zâram.
In Arnor a single five-pointed star became used as a device, the Elendilmir, representing the Star of Earendil. In Gondor the device including the stars and the Silver Crown fell out of general use, until the time of Elessar and the Reunited Kingdom (from LOTR Index IV-"star").
The crown of Gondor is depicted most clearly in letter 211 of Letters of J.R.R. Tolkien. The tree emblem cleverly adapted by WETA is a depiction of a nearly discarded description by Tolkien himself.
While the Stewards (at least those depicted in the film) were seen with variations of Gondor's White Tree emblem, they had no real emblem of their own. Tolkien describes their banner as being plain white, perhaps representing their non-descript position as guardians of the throne and/or or the purity of their loyal service. However, the Stewards did have a seal in Tengwar lettering that simply said "steward". It was crowned by only three stars.
I thought these might represent three Gondorian palantiri, but I can only surmise which palantiri the three stars of the Stewards represented:
Of the seven "famous" palantiri (those of Osgiliath, Annuminas, and Aman Sul) were destroyed according to various of Tolkien's notes and tales. There were also the three stones of Minas Tirith, Minas Ithil (Barad-dur), and Orthanc. The seventh stone of Elostrion was kept in the Tower Hills (Shire area) and sailed with the Ringbearers at the end of the War of the Ring. At the time of Elendil, the three stars of the Steward's "most probably" represented Minas Ithil, Osgiliath, and Minas Tirith.
To the best of my reckoning, the emblems used in the films (see post #1 for links) could be explained as follows (some of these observations have already been made by other members):
1) Boromir's tree with leaves might represent the Steward's (or Gondor's) hope for the salvation of Gondor, that the kingdom would again flourish. This would be very much in keeping with what Boromir is known to say throught FOTR (particularly what he says at the Council of Elrond and again to Aragorn in Lothlorien).
2) Faramir's tree is an older generic emblem (since Denathor did not find much favor with his second born, there might not have been anything special afforded to him in the latter days). It has seven stars-- six in silver and the seventh etched in leather overlay (top-center beneath the chin).
3) Pippin's tree is a trickier muse. We know his armor once belonged to a young Faramir. The two stars relocated to stand beneath the tree
could have had a secondary significance besides the palantiri if one considered that they might have represented the two sons of the Steward. None of this cannot be confirmed, but it is easy to imagine from Gandalf's words that Denethor might have been less obnoxious to a younger Faramir, and decorating his first armor as a sort of first rite of passage. The five stars remaining above the Tree might have simply been the best or only possible remaining location for them.
4)
THIS design (with or without the crown) was seen carved into the walls of the Minas Tirith throne room throught ROTK. This could have been an architectural modification- a different interpretation of the emblem made by the imaginary designers of Minas Tirith. Not the official confirmation I'd hoped for, but I'll go with it for now.
5) Elessar's armor and Arwen's standard have been explained-- the crown was reserved for the heirs of Elendil, not used after Isildur, and revived with the return of the king at the end of the Third Age.