Here’s an update: after playing a little more, I noticed that the intonation is actually pretty bad. Some notes are flat or sharp by as much as 12 cents (!) I’m not sure whether changing the gaps changed the tuning, but I don’t think that’s the main source of the problem since most of the motes are pretty off (and in wildly inconsistent directions) and I only dramatically changed the gaps on some notes.
So I’m now in the process of tuning it, using the scraping method. I practiced again on the El Cheapo, which I was able to get pretty well in tune, and now I’ve progressed to the M37C. Most of the reeds need tuning changes. I’m going to a tolerance of +- 3 cents, which is what I did on the El Cheapo and that seems to make melodies sound right and chords not crunchy.
In general, I’m really glad I started playing the melodica as an instrument and I’m learning a lot with my practice sessions (mostly on the instrument I already tuned for now). I definitely think it’s not at all deserving of its reputation as a child’s instrument and I think it should get more serious consideration