First off, the H9 doesn't load anything when I play the Sysex track in Logic. I should probably do something else to prompt the load?
It seems to me that for the three major live projects I'm involved in, I should purchase three separate H9's, or a dedicated MIDI switcher, whichever option is cheaper…
The manual says that "The H9 must be set to the desired SysEx ID number" in the "Restoring Presets and System Setting" section. Did you do that before sending the sysex track? The H9 Control also has a feature of "Import presets or preset lists" in the settings page, where you can import a sysEx file. Have you tried that?
Anyway, as camn and yourself suggested, I think the best solution for your purpose would be getting a dedicated MIDI switcher.