OK, I finally got a little time to work on this one.
This one isn't that deep of an inquiry, considering that the text in question addresses a geographic location.
Firstly, due to the name it would have been of value in the greater region of Macedonia/Athens in general, or it would have been of value to some group who valued the Macedonian/Athenian regional variation of Christianity as a form of authority or example to follow; we can't be completely certain which would be the case on the face of it.
Second, we need to look at the concepts expressed in 2TH and see which other text is sympathetic to these forms of concepts; are the alike Pauline, Johanist/Danielic, Markian, "Gnostic", or other concepts?
2TH makes it pretty easy, actually.
We have a really good sample right at the beginning.
For now, the NIV version:
The Judgment at Christ’s Coming
5 This is evidence of the righteous judgment of God, and is intended to make you worthy of the kingdom of God, for which you are also suffering. 6 For it is indeed just of God to repay with affliction those who afflict you, 7 and to give relief to the afflicted as well as to us, when the Lord Jesus is revealed from heaven with his mighty angels 8 in flaming fire, inflicting vengeance on those who do not know God and on those who do not obey the gospel of our Lord Jesus. 9 These will suffer the punishment of eternal destruction, separated from the presence of the Lord and from the glory of his might, 10 when he comes to be glorified by his saints and to be marveled at on that day among all who have believed, because our testimony to you was believed. 11 To this end we always pray for you, asking that our God will make you worthy of his call and will fulfill by his power every good resolve and work of faith, 12 so that the name of our Lord Jesus may be glorified in you, and you in him, according to the grace of our God and the Lord Jesus Christ.
First, does Paul talk this way?
Does Paul talk of angels like a nuclear missile threat, and does he don the fire and damnation pre-Calvinist attitude that we find in the interpolated ending of Matthew, the book of John, and the book of Revelation?
Does Paul talk of being worthy of his god in such a manner as to convey the notion that one is practically damned with a very thin chance of survival?
To compare, we can use the uncontested Pauline texts.
Running a comparison there, we do not see these forms of discussions.
This entire section doesn't even really sound like Paul; Paul gets angry and definitely is strong in tone for reprimand, but he's not found stamping such a strong damnation on humanity outright all over the place in such a way as to just write lengthy paragraphs about how terrible humanity is, how unworthy they all are, how slim of a chance anyone has, and just how thoroughly thrashed to pieces all others will be.
Also of note, Paul never makes a comment about mighty glory of his god, nor talk about the idea of Jesus coming from the heavens with angels in a fire.
On the other hand, these concepts readily exist in Daniel and Revelation.
Essentially, 2TH, to me, looks like an Asia Minor Daniel-family apocalyptic text; which is a group quite sympathetic to Pauline concepts, but also a group whom heavily modified the contents they acquired with much more severity and cosmic opera.
In this group, Jesus becomes a weapon more often than a binder.
For Paul, most often, Jesus is a binder and that is the strength of Jesus - not so much a discussion about Jesus as if Jesus was the big brother who returns home and makes everyone regret picking on you.
Now, the question in regard to the comparison between HBK and 2TH in tonality:
HBK definitely would be possible as a cultural influence, as the Asia Minor group was definitely familiar with the Septuagint variation of Daniel, which would mean their HBK would be the Septuagint variation as well, most likely.
Why would they write this as TH in Asia Minor?
Well, this is also the likely group region for the book of John and possibly long-form Mark (the more cosmic Jesus resurrection).
John owes a large amount of itself to Luke, and the book of Luke is very likely from the Athenian region; based on the high quality of philosophical concepts explored.
Asia Minor appears to regularly borrow from some source as the basis, and then create their own version which almost exactly mirrors the inspiration, but then strongly goes in a new direction than the other, and typically does so in a very Calvinistic apocalypse rendition.
So essentially, everything fits easily with this same group.
They value the Athenian and Macedonian regions for impressions of example and/or authority, carried the same flavor of extreme hell-fire damnation vengeance talk, and had the Septuagint early on, and were also a region which was rather known for extreme measures in their religious expressions (christian or otherwise).