"Every" and not "the whole" is the correct translation here. The phrase in Greek, as you quoted, uses the word πᾶς and not ὅλος (as in ...the whole body shall be full of light - Matthew 6:22). So any exegesis based on an understanding that Paul is referring to a single family and not many families misses the mark, I think.
I do not think "fatherhood" is the correct translation here. The Greek word - πατριά - appears only in two other places in the New Testament, but it occurs over 150 times in the Greek Septuagint. In no place is it used to indicate the abstract quality of "fatherhood". It is almost always used to mean "family" and sometimes "tribe" For example:
καὶ ὁ ἄρχων οἴκου πατριᾶς τοῦ δήμου τοῦ Γεδσων Ελισαφ υἱὸς Λαηλ.
And the ruler of the household of the family of Gedson was Elisaph the son of Dael (Numbers 3:24 LXX).
The meaning of the verse is that every family and lineage on earth -
Gentile and Jew alike - proceeds from the Father above, as likewise do the angels in heaven. Theophylact presents the patristic consensus:
He explains that every family [πατριά] and lineage proceeds from the Father [πατήρ] above. And the generations of men on earth he calls "families" because they are named after the founding fathers of their lineages. But in heaven, although no angel begets or is begotten of another, he also applies the name "families" to the constituent bodies and ranks of angels. Thus God the Father Himself created every family in heaven above and on earth below; and everyone called "father" derives that name from Him.*
You will find similar interpretations in the commentaries of Theodoret, Jerome, and John Chrysostom (two Greeks and a Roman educated in Greek - all 4th/5th c.).
Although I have not run across this in any commentary, it seems to me that Ephesians 3:14-15 perhaps points to the correct understanding of Matthew 23:9 (Call no man your father upon the earth; for one is your Father, which is in heaven.)
* Explanation of the Epistle to the Ephesians, tr. by Christopher Stade, Chrysostom Press, 2013, pp.49-50