It sounds like you have everything hooked up correctly. At this point you have two options; make your source louder, or increase the gain on the amplifier.
The VS1053 used in the Music Instrument Shield does have a volume control register that can make it louder, but unfortunately you can’t access that register from the Music Instrument Shield (the MP3 Player Shield, based on the same chip, has a more complex interface that does allow this). So you’re correct, in your case changing the MIDI volume is about all you can do to make the source louder.
If that’s not enough, you can increase the gain on the amplifier board by adding your own gain resistors. The Quickstart Guide at the top of this page has instructions. This will make the amplifier considerably louder and I think will solve your problem. Let us know if you have further questions!