However, can you explain why Schoner would have made the mistake of portraying TA as a solid land mass (1524) and the Europe as this very same continent (1515)? It does not make sense to me.
I'm assuming you are asking why he transitioned from his 1515 and 1520 C-shaped world maps—which are nearly identical except that Spain has been adjusted to better represent Spain—to his 1524 solid landmass resembling Antarctica.
In answering this it is important to point out the documented methodology of another early 16th century cartographer, Piri Reis.
An inscription on the 1513 Piri Reis World Map openly boasts scaling old maps—some claimed to have been composed in the 4th century BC during the reign of Alexander the Great—to new maps:
No one now living has seen a map like this. I have composed and constructed it using about twenty maps and mappaemundi; these are the maps which were composed in the time of Alexander of the Two Horns, and which show the inhabited portion of the earth.(1) The Arabs call these maps ja'fariya.
I have used eight ja'fariya map, an Arab map of India and four recent Portuguese maps - these maps show the sea of Sind (Sindhu-sagara), India (Arabian Sea) and China according to mathematical principles(2) - and also a map of the western regions drawn by Colombo (Columbus). The final form was arrived at by reducing all these maps to the same scale(3). Therefore the present map is as accurate for the Seven Seas as the maps of our own countries used by sailors.
- So the first thing we notice is that he references both recent and very ancient maps to piece together his 1513 map. Meaning in 1513 Reis had access to a collection or library of many various maps.
- Some of Reis' source maps may not have been charted using "mathematical principals." Some maps like the mappae mundi and early Greek maps likely were not delineated with latitude and longitude.
- Various features from multiple source maps, many of which were likely lacking delineations which would have proven a useful guide for scaling, would have been aligned and scaled by approximation together into one map.
Okay so fast forward
JUST TWO YEARS to 1515. Schöner is building a custom globe and is tasked with incorporating a purported strait discovered in 1508. This actually would turn out to be a bay, but those who reported it engaged in a little hyperbole suggesting it was far more than a bay and the southern shore of this supposed strait was a wide ranging coastline similar to North Africa's Barbary Coast.
This over exaggerated report may be the sole reason large renditions of Terra Australis Incognita suddenly appear at the turn of the turn of the 16th century, including Schöner's depictions.
Like Piri Reis, we know Schöner, a highly educated mathematician and skilled cartographer, had access to many source maps. He perhaps rummages through some ancient maps and stumbles upon a set of very similar maps (source maps for his 1515 and 1520 designs) without delineations of longitude and latitude, because Roman maps like Agrippa's did not require them. One of the maps, perhaps a map in the early stages of completion, still has visible circular guidelines—similar to
the image in my post above—showing its concentric nature.
Schöner is searching for a large continent and here he finds a map drawn around a central point and grid that shares a similarity with the southern projection of a globe. Even more compelling, the map depicts the English Channel which to Schöner meets his need for a strait. Like Reis he scales the landmass onto his globe, in this instance by centering its concentric design over the South Pole while placing Britain so as to represent the tip of South America and the English Channel becoming Magellan's strait. Five years later, 1520, he makes another globe and opts for the alternate design, not certain which one is the more accurate depiction.
Jump ahead again, this time to 1524, and Schöner is creating another globe, but this time his earlier versions of the continent are no longer the perfect match. Magellan's voyage discovers a deep bay in the midst of his new found strait, a feature not present on the strait depicted on either of Schöner's previous source maps. Magellan's voyage also introduces two other new discoveries, a pair of islands the crew names the Unfortunate Islands.
Carrying over the now common misconception of a large continent lying beneath South America based on the earlier purported find, Schöner, apparently following the same methodology previously utilized by Reis and himself, searches again for a map of an unidentifiable land that could possibly match these latest discoveries.
In his search he comes across the map of a landmass with two small lone islands set off its coast, perhaps setting off an alarm. He is now thrilled to have found a possible ancient representation of the Unfortunate Islands nestled alongside a large landmass. Unfortunately the large landmass does not have a depiction of the South American continent butting up against it to form a strait, but there is a depiction of Atka Bay that could correspond to the bay within the strait.
The ancient map of Antarctica, lacking any delineations or any that Schöner was familiar with, was subsequently aligned and rescaled to place the islands high in the Pacific to represent the Unfortunate Islands and Atka Bay at the tip of South America to form Magellan's strait complete with a large southern bay. You may have already seen the image below which portrays modern Antarctica sitting alongside a combination Finé/Schöner. Perhaps most amazing and lending credibility to my theory is the fact that Schöner's depiction is virtually identical to Carney and Siple Island lying along the flattened end of Western Antarctica, but looks very little like the actual Unfortunate islands which were much much further apart both vertically and laterally. He apparently opts for the source map's design over the description provided by Pigafetta and others who logged the voyage.

Most interesting and perhaps a bit ironic, you of all people should be able to accept the possibility of Schöner retrofitting ancient maps to modern maps, for you have used virtually the same methodology in realigning and rescaling Schöner's southern landmass to fit Australia, New Zealand and as your last post points out, Antarctica.
-Doug