This is a great topic!
Thank you for the compliment on "What Child is this".
Well, a few thoughts come to mind about arranging for Theremin.
~~ melodic writing suits the Theremin well ~~
The Theremin is a melodic instrument.
A Theremin creates harmony only through the use of multi-track recording, echo loops, pitch-shifters, or multiple Theremins.
To play a rhythm part is outside of the Theremin's primary language, too. While Pamelia Kurstin can make the room dance with her amazing walking bass technique, you probably don't want to assume that the Thereminist that will play your arrangement is similarly gifted. (i.e., the Thereminist you arrange for may be YOU! Of course, one can decide to push the envelope.)
~~ what kind of melodies ~~
1) The theremin can play the theme -- that is the actual notes of the song.
2) The theremin can play a descant while another instrument or Theremin plays the theme. The best descants are rhythmically independent from the theme. That is, when the theme has a long note or a rest, the descant plays lots of notes... when the theme is moving, the descant holds a note or doesn't play at all. (the descant to 'Angels We Have Heard on High' is an excellent example).
3) The theremin can play a variation on the Theme. A good example is Peter Pringle's remarkable arrangement of "Away in a Manger" wherein he adds arpeggios and grace notes to the melody when he plays the second verse.
Other uses are possible however I personally have utilized the above methods.
~~ difficult but doable ~~
1) close harmony / block chords are difficult because of the tuning. You might confuse another player's (track's) note with yours and go off into "cloud cukoo land" trying to correct it. I have experimented with such arrangements however have created nothing that I'd want anyone to hear. I have not tried this with a pitch preview -- a pitch preview might help to pick out my Theremin note from the others.
2) Unison notes on multiple theremin tracks... very difficult because if they are out of tune, it is really really noticeable. And while playing, it is hard to tell your note from the other. If the other note is sharp, and you hit your note flat, you may "hear" the sharp note, and correct downward, making your flat note even flatter. If you MUST have a unison, have one player hit the note first, then the second one. If they both hit the same note at once... beware! I imagine this could get dicey with two Thereminists at once -- each mistakenly correcting the other's note! (kind of like the practical joke when you switch the controls on someone's two-sided electric blanket...)
3) Wide spacing works best! If the two Theremin tracks are widely spaced, then the difficulty of discerning your note goes away. A melody with a descant playing an octave or two higher is pretty easy to bring off.
~~ arranging for an audience ~~
Usually when I start, my first thought is the style of the arrangement. Will I do something traditional or wildly contemporary? Will I use sound effects. Will the rhythm be steady or rubato? The other question is what do I want to give to the listeners? Do I want to amuse/entertain? Do I want to pour my heart out? Do I want to deliver some kind of technical tour-de-force? Am I doing an "etude" -- a work to challenge myself somehow? How do I deliver a performance that appeals to mind, body, and heart?
I know this is all philosophical however arranging is 1% inspiration, 99% perspiration. The 1% inspiration is essential, just like the pinch of salt is necessary in many recipes. Just gotta have it or there is no flavor. If you are reading this you already know that anything worth doing requires the "grunt work". Fortunately, arranging music is a fulfilling way to break a sweat! :)
The good news in all this is that we can safely assume that the audien