The Shelatim of David and the Magginot and Tsinnah of Solomon
I think the source of confusion is mixing the different words translated as "small shield": magen and shelet.
The mysterious shelet
shelet only appears 7 time in the OT and there is some doubt as to whether it refers to a small circular shield or a quiver.
Here it NIDOTT:
ANE This word is of rather obscure etymology but is likely connected
with a verbal root attested in Akk. (šalāṭu) and Arab. (salaṭa). The
exact nuance of this term escapes us, so it is safest to translate
generically as “shield.”
OT The term occurs only 7× in the OT, 3× with מָגֵן (2 Chron 23:9;
Song of Songs 4:4; Ezek 27:11). In all other cases, שֶׁלֶט refers to
the military weapon and is never used in a metaphorical sense for
God’s protection (see 2 Sam 8:7 = 1 Chron 18:7). The word is often
used in contexts where shields are placed on ornamental display. That
the word means “shield” is certain in a passage like Song of Songs
4:4, where the parallelism clearly intends a near synonym of a
narrower meaning to מָגֵן, the most common term for shield. However,
Borger (1972) has marshaled evidence from the versions and cognates
that the word means “quiver” in Jer 51:11. Thus, NRSV so renders in
that and other passages (cf. Ezek 27:11). For full discussion of the
issue see Holladay (422–23).
VanGemeren, W. (Ed.). (1997). New international dictionary of Old Testament theology & exegesis (Vol. 4, p. 125). Grand Rapids, MI: Zondervan Publishing House.
Whatever the shelatim were, David captured an unspecified number of gold shelatim from the Syrians, together with a large amount of bronze, and carried these back to Jerusalem. See 2 Sam 8.7 and mirrored in 1 Chron 18.7
Judah now has an unknown number of gold shelatim and a lot of bronze.
Magen and Tsinnah
magen is widely used in the Old Testament to mean "shield" (that you carry).
tsinnah is a standing shield (covers from head to foot). It only appears twice in the OT.
Solomon made 200 gold tsinnah and 300 gold maginnim as described in 1 Ki 10.16-17 and paralleled in 2 Chron 9.15-16.
The 300 gold magginim of Solomon were taken by Shishak as described in 1 Ki 14.25-27 and paralleled in 2 Chron 12.9-10. In the same passage, Rehoboam replaces the maginnim with versions made of bronze. No mention is made of the 200 large standing shields -- were they taken? Where they replaced? The text doesn't say and they are not mentioned again.
It happened in the fifth year of King Rehoboam that Shishak the king
of Egypt came up against Jerusalem, and he took the treasures of the
house of Yahweh, and he took all the treasures of the king’s house. He
took the small gold shields [maginne] that Solomon had made, so King Rehoboam
made small copper shields [maginne] in place of them and entrusted them to the
commanders of the royal guard who keep the doorway of the king’s
house.
Thus Isreal is missing its 300 gold magginim, which have been replaced with newly created bronze versions, but Israel still has an unspecified number of gold shelatim that David captured frm Syria, and may or may not have the 200 gold tsinnah that Solomon made.
In 2 Chron 23.9, Jehoida gives the 300 (bronze) [maginnot] made by Rehoboam and the unspecified number of gold shelatim that belonged to David, and distributed them to the commanders of the hundreds:
And Jehoiada the priest gave the spears and the large shields
[maginnot] and small shields [shelatim] that had belonged to King
David that were in the house of God to the commanders of hundreds.