The preview image at TrekCore
includes a glimpse at the orchestra list for "City on the Edge of Forever," and there are a few woodwind performers listed.
I hadn't seen that! Thanks for linking.
That preview image contains a listing that includes Way To Eden. Far Out Jam! Headin' Out To Eden! And the instrumental tag over the death of Adam. The music editor put a little sting at the moment where the "dead" Adam twitches his finger, which is such an oddball decision that it seems like genius.
I can't believe I'm excited about that. Part of it is just (finally!) having all the questions answered.