Also found a book "The Music of Star Trek" by Jeff Bond. It has the Apollo Motif in it in some form. I'll have to look into that. it maybe all I need.
On p. 25, there is a reproduction of the first page of Fred Steiner's handwritten sheet music for "Apollo Motif." It's also mentioned in the cue sheet for the episode on pp. 47-8 (listing all the cues recorded for or tracked into the episode and their running times), and there's a brief discussion of it on p. 73 in the interview with Steiner (basically just saying that its use of an open-fifth interval is an "old stunt" for evoking ancient times, and that "Adonais" was Steiner's favorite of his TOS scores).