Catalin Anghelina's study "The Ancient Representations of the Titan Atlas" is almost precisely what you're looking for. It largely focuses on the differing appearance of Atlas in Greek art itself, and identifies the same contrast you do.
The first thing to note is that there are differing accounts of what, precisely, Atlas was sentenced to. There's the Homeric (and more popular) account, "that he holds the pillars which keep earth and sky apart." And there's the Hesiodic account, that he "Atlas holds the sky with his head and hands while being located in Tartarus in front of its doors."
Deceptions in the style of Homer are admittedly less common nowadays, but there is ample representation of them in antiquity. For example, "on a Laconian cup which is dated before 550 BC [...] Atlas stands on a Doric column supporting a sky made of concentric [...] zones studded with stars."
However, such an image makes little sense in the Hesiodic depiction. After all, "Atlas is located in Tartarus, which in the Greek myth is clearly located under the earth" and so "it is not possible to view the Hesiodic Atlas as supporting the sky from between earth and sky."
The Hesiodic account, as you may have guessed, is the one that leads to the depictions of Atlas you highlight in your question. Anghelina dates it back to at least 450 BC, where it appears (admittedly, in a depiction of Herakles, not Atlas) on a Campanian amphora.
How did these two depictions of Atlas originate? Obviously there's no definitive answer, but Anghelina's looks to the presence of analogous characters in other contemporaneous religions.
There is the Vedic God Vishnu, whose dwelling place is at "the North Pole of the sky." But there is also another form of Vishnu: as described in Wilson's translation of The Vishnu Purana, "Below [...] is the form of Vishnu [...] which is called Śesha [...] Śesha bears the entire world, like a diadem, upon his head." Śesha, symmetric to Vishnu, is located at the world's southern pole -- as Atlas is most often portrayed.
There is also Shu, of Ancient Egypt, who separates the sky (Nut) from the Earth (Geb). Depictions of Shu "[are] similar to the Homeric one: the god, who symbolizes the axis mundi, holds the sky from the inside," as seen in this image.
Anghelina thus concludes:
Since in the Hindu myth the god who is located at the North Pole, Vishnu, is most likely of a non-Indo-European origin, the conception of a god located at the celestial South Pole and holding up the sky from there is also likely to be of non-Indo-European origin. Traces of this myth can be found in the Altaic cultures of Siberia, where such mythologies of the North Pole have been documented. It is in these shamanistic cultures where the most plausible candidates for the origin of this type of representation must be looked for. One cannot say, therefore, that this Greek type is recent borrowing from the Mediterranean/Near East sources. Both representations of Atlas coexist from before the time when the Greeks entered the Greek peninsula. Thus, the Hesiodic representation of Atlas, the 'Farnese' Atlas, may be very old, possibly going back to the period when the Greeks were still in contact with the shamanistic cultures of Asia."
Anghelina C. The Ancient Representations of the Titan Atlas. Museum Helveticum. 2010 Dec 1:195-206.
Wilson HH, editor. The Vishńu Puráńa: a system of Hindu mythology and tradition. J. Murray; 1840.