Love this - especially the Song mechanics. The only downside is now I want to rewatch Symphogear, and I don't have time for five seasons of anything right now. :)
Couple of bits that feel like they're missing from the book off the top of my head:
- you mention a map is recommended; a few pages on drawing (zone-based?) maps would be a good thing to include.
- a page or two of advice on which hymnal type/song combos go well together would be great for new players.
As a side note - have you considered having a set list of advances for each hymnal type? i.e. just ordering the basic upgrades in slightly different ways for each class (and having the different types have the ability to take different upgrades twice or not at all).