I have seen Jimmy Akin use this argument, and I think he is basing it in part on the first Canon of the Seventh Ecumenical Council. That Canon does not specify the Council of Carthage, but it appears to confirm the decrees of prior local synods in general, of which Carthage was one. Here are its words: [We] press to our bosom with gladness the divine canons…whether they have been set forth…by the Six Ecumenical Councils, or by councils locally assembled for promulgating the decrees of the said Ecumenical Councils. (Canon 1) The article
here defends this perspective.
It is also noteworthy that Nicea II quotes the Book of Sirach: “[The Iconoclasts] not only detested the pictured images, but also set at naught all decorum, being exceedingly mad against those who lived gravely and religiously; so that in them was fulfilled that which is written, The service of God is abominable to the sinner.” (Canon 16, quoting Sirach 1:25)
Wow! Thanks, that nails it.
If it’s of any use to you I did a little digging on Medieval use of the deuterocanonical books, and discovered some things. Aquinas’ use of them is well known. Below are some others.
St. Bernard of Clairvaux (1090-1153) quotes the deuterocanonical books as Scripture.
On Love of God: IV,13 (Wis 9:15), VII,23 (Sir 45:6; 18:30), XII,35 (Wis 11:21). Letter 3,1 (Sir 30:23); Letter 15,2 (Wis 3:1); Letter 35 (Sir 3:8); Letter 42,2 (Sir 2:12).
De Consideratione I,5 & 9; II,13 (Sir 38:24f); III,2 (Wis 1:1); IV, 2 “Scripture assures us” (Wis 10:17); IV,6 (Bar 3:24).
Richard of St. Victor (+1173)
Twelve Patriarchs (Chap. 1) Wis 7:29; 8:1-2; 7:10; (3) Wis 1:1; (20) Wis 1:5.
Mystical Ark (I,1) Wis 7:30; 9:19; 8:1; (II,7) Wis 7:17,21; (II,15) Sir 24:15,20; (III,13) Bar 3:11.
St. Bonaventure (1217-1274)
The Journey of the Mind to God (1,15) quotes Wis 5:20. In
The Tree of Life (2,5) Sir 10:9; (9,35) Wis 7:29, Tob 13:20. In the
Life of Francis (Prologue, 1) Sir 50:6,8; (1,1) Sir 45:1 & 31:8.