@Noah Brode
It's OK. I couldn't open the pdf in the post... But I got the email. By the way, when you upload a pdf file, if you pick the + sign, the pdf is inserted in the post and works...
I know that Messiaen is "too big" to get his theory in a post, but I think the idea is working with different scales and building harmonic systems different from major / minor.
Mode 2 is very "rich" for melodies. You've done it quite well. The motif is beautiful because of the rhythmic figures. The scale is fully presented in the first measures, which is good, more important for solo melodies. You've worked it mostly with transpositions and some inversions. And, although the whole scale is used, the impression is rather tonal. That's what Messiaen said, you can use these modes in a wide range from tonal to atonal. In fact, there is a constant center: C. Some fragments sound cadential (m. 5-6 ending in Db...), going finally to C. Of course this nice motif could be fully developed (inversions, rotations, etc...). These are tools that those composers used. But the result is coherent, sounding like a folk scale, very expressive and intense. Nothing to object. Just that there are almost opposite ways to use this mode (not so tonal).
Mode 3. In this case, the result is more contemporary. You've managed very well harmonizing the melody with the same mode. There are more contrasting motives in the melody, with nice transpositions downwards. The effect in m. 27-29 is great. Notice how the final chord is a Cm(maj7).... It's fine to combine non tonal elements and triadic chords. On the other hand the use of dissonance ("color", said Messiaen) is good: for example m. 29 (F#, Ab, C, D...).In summary your way was the one based a little bit on the classic development of the melody. The result is licit, of course. Perhaps in a course on contemporary techniques you would be asked to stay away from the "tonal" mood. As you mentioned, there is a lot of contemporary techniques that can be used to sound more or less classic....
One way to make the harmony richer and sound less tonal is, as I told Maarten Bauer, to add deep notes (as pedal notes) in the piano. Notes of the scale, of course, but different from what is sounding up above. So, you create two layers of tone centers.