To summarize, Spotify can of course terminate any API they so wish, and there is absolutely nothing in GDPR that compels them to keep it up. As long as they of course still follow the requirements by GDPR. As annoying as a workaround would be for Confiks, emailing the data within those 30 days to SongShift is acceptable and in compliance. There is nothing in GDPR that says "data transfer options once enabled cannot be removed and/or changed".
Quoting the clause "the data subject shall have the right to have the personal data transmitted directly from one controller to another, where technically feasible.", always seemed off with what is being demanded, because, they would be complying with that requirement by compiling and archive of the data, a big dump, and send it to SongShift. "I demand that you re-enable the API", on the other hand has no basis whatsoever in GDPR. The quote follows with "... or allow for some other method to allow me to exercise my rights under the GDPR", which is exactly right.
Spotify re-enabled the API because they chose to, not because they had to.
To clarify: I think it was great that Confiks convinced Spotify to re-enable the API. But, the arguments presented were not particularly convincing, and I took this as a case of Spotify doing the right thing, rather than a "David vs Goliath".