Is the Manias version of "Sanki Tousen" available as a single?
And alas, it turns out the answer to my question is that the Manias version of "Sanki Tousen" will indeed not be made available for sale. The comments on the official YouTube upload of the TV-sized Manias version of "Sanki Tousen" say as much:


  ※こちらの「まにあーずver.」の楽曲はアニメ放送用の音源を特別に掲載しております。
  　CDには収録されませんので、ご了承ください。


(Roughly: "This is a special upload of the "Manias version" of the song, using the audio from the television broadcast. Please be aware that it will not be included on the CD.")

What a shame.