Does H9 send the corresponding MIDI CC values out of its MIDI Out, then? That could make things a bit easier.
Yes, you can configure it to do this. If you go into the system settings on the H9 itself, you'll need to set CTL.XMT to On. It's a setting under the MIDI settings section. The H9 user manual explains how to get into the H9's system settings on the H9 itself: