For whom was Bilbo’s mithril coat forged?

[Alcuin]

In Chapter 16, “A Thief in the Night”,

The Elvenking looked at Bilbo with a new wonder. “Bilbo Baggins!” he said. “You are more worthy to wear the armour of elf-princes than many that have looked more comely in it…”

and in Chapter 13, “Not at Home”,

[Thorin] put on Bilbo a small coat of mail, wrought for some young elf-prince long ago. It was of silver-steel which the elves call mithril, and with it went a belt of pearls and crystals.

Now of this second passage, Douglas Anderson in The Annotated Hobbit remarks in footnote 2 to this chapter that,

1937:”It was of silvered steel and ornamented with pearls, and with it went a belt of pearls and crystals” > 1966 Ball[antine]: “It was of silver-steel, which the elves call mithril, and with it went a belt of pearls and crystals”

This revision introduces the name mithril in The Hobbit and brings the description of Bilbo’s mail-coat into accord with that in The Lord of the Rings. …

These descriptions of Bilbo’s mithril mail match Aragorn’s reaction in Chapter 6, “Lothlórien”, in Fellowship of the Ring:

Here’s a pretty hobbit-skin to wrap an elven-princeling in!

However, in Chapter 12, “Inside Information”, Thorin and Balin recalling the treasures of Thrór mention (emphasis mine)

the necklace of Girion, Lord of Dale, made of five hundred emeralds green as grass, which he gave for the arming of his eldest son in a coat of dwarf-linked rings the like of which had never been made before, for it was wrought of pure silver to the power and strength of triple steel.

Is this “coat of dwarf-linked rings … wrought of pure silver to the power and strength of triple steel” Bilbo’s mithril coat? If not, then for whom was the mithril coat forged? Legolas? And how many child-sized mithril coats are there? for if this is not the same as that made for Girion’s son, there must be two child-sized mithril coats.

Thrór returned to Erebor about 350 years before the events of The Hobbit. That would make Legolas very young indeed (for an Elf) had the coat of mail been forged for him: else, the Dwarves would surely have delivered it to Thranduil. By the same token, were the mail forged earlier than that, during the sojourn of Durin’s Folk in the Grey Mountains for instance, some 400 years earlier, it does not make sense that they would have failed to deliver the mail for centuries upon end while hauling it around.

Surely it stands to reason that the mithril armor was forged for the son of Girion Lord of Dale, paid for with Girion’s emerald necklace, and delivery was interrupted by Smaug’s arrival. The magnificence of the artifact was such that Thorin, the Elvenking, and Aragorn assumed that it must have been for an Elven-prince – unless, of course, they knew it was, and for whom it was made, in which case Legolas is an awfully young Elf.