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As for the "natural completion of set theory axiom systems" phrase, Gödel appears to paraphrase it in a conversation with Wang recorded on p. 261 in Wang's 1996 Logical Journey book in a way completely consistent with Gödel's Cantor 1947 paper in that both the axiom of constructability and an axiom that refutes GCH are considered (and rejected) as new axioms. The proposition that all sets are constructable is a natural completion of subjective set theory for human beings. Ronald Jensen has shown that it leads to unnatural consequences such as Souslin's hypothesis...The "axiom" of determinacy is another example which in its general form contradicts the axiom of choice.

As for the "natural completion of set theory axiom systems" phrase, Gödel appears to paraphrase it in a conversation with Wang recorded on p. 261 in Wang's 1996 Logical Journey book in a way completely consistent with Gödel's Cantor 1947 paper in that both the axiom of constructability and an axiom that refutes GCH are considered (and rejected) as new axioms.

The proposition that all sets are constructable is a natural completion of subjective set theory for human beings. Ronald Jensen has shown that it leads to unnatural consequences such as Souslin's hypothesis...The "axiom" of determinacy is another example which in its general form contradicts the axiom of choice.

Although Godel, in the perception of concepts section of Wang 1974, does not come out and say his views were same in 1938 he apparently does advise not to be mislead by a misinterpretation of “vague concept” into using Godel 1938 as evidence against Godel being a concept Platonist in 1938 (as his vague concept epistemology implies his concept Platonism). This advice was apparently directed to Mostowski but it also clearly applies to Davis in his influential paper. If so that removes one big argument against Godel not being an early Platonist, unless correspondences prove otherwise.

Although Godel, in the perception of concepts section of Wang 1974, does not come out and say his views were same in 1938 he apparently does advise not to be mislead by a misinterpretation of “vague concept” into using Godel 1938 as evidence against Godel being a concept Platonist in 1938 (as his vague concept epistemology implies his concept Platonism). This advice was apparently directed to Mostowski but it also clearly applies to Davis in his influential paper. If so that removes one big argument against Godel being an early Platonist.

Although Godel, in the perception of concepts section of Wang 1974, does not come out and say his views were same in 1938 he apparently does advise not to be mislead by a misinterpretation of “vague concept” into using Godel 1938 as evidence against Godel being a concept Platonist in 1938 (as his vague concept epistemology implies his concept Platonism). This advice was apparently directed to Mostowski but it also clearly applies to Davis in his influential paper. If so that removes one big argument against Godel not being an early Platonist, unless correspondences prove otherwise.