Use H2's small build target
H2 provides a 'jarSmall' build target that produces a smaller jar containing fewer optional features and resources. The smaller jar includes everything we need, and would reduce our APK size by around 500 k. Unfortunately it's not available from JCenter.
Removing the unneeded features and resources with ProGuard isn't simple, as most of the savings come from resources in a zip file embedded in the jar.