My guess is AN 6.38 is not about selfhood.
There are no hidden & different teachings found in obscure & unimportant suttas, like this one. When a sutta like this is difficult to understand the problem or issue is generally with the translation.
The 1st step in unraveling a sutta like this is to identify which party established the definitions or parameters. In AN 6.38, as expected, it was the Brahman that established the definitions, with his terms: attakāro & parakāro. In other words, we should not assume that these terms reflect the same understanding of 'atta' as held by the Buddha. It is not the Buddha using these terms but the Brahman using these terms.
This is exactly the same as the unimportant SN 44.10, which so many people get stuck on in a wrong way. In SN 44.10, it was the wanderer Vacchagotta that established the definitions when asking: "Does a self exist (atthattā); does a self not exist (natthattā) ". The reply of the Buddha in SN 44.10 is completely unrelated to the Buddha's teachings of anatta & sunnata. The reply is the same as when a small child asks: "When will Santa Clause come?" and the parents answer: "At midnight, dear" (despite Santa Claus not even existing).
Therefore, in AN 6.38, the term 'selfhood' is probably used as the Brahman understands selfhood. The word "atta" is probably understood & used by the Buddha in conventional language, such as found in the Attavagga of the Dhammapada, which states: "self is the refuge of self". In the Attavagga, the "atta" is just conventional usage (rather than a real self).
The 2nd step in unraveling is examination the core issue or message, which is about the elements of initiating, exertion, effort, steadfastness, persistence, endeavoring, moving forward & moving back.
Therefore, the original statement is probably about the word "kāro" (rather than about the word "atta"). The Brahman was probably saying: "There is no kāro in onself or in others" and the Buddha replies: "There is kāro".