Still no resolution, but I wanted to update with other things I've tried since the original post:
Changed MIDI channel to Omni so that it should respond regardless of what channel is transmitted
Connected both the HX Stomp and the Chocolate Plus to my computer and ran a MIDI tester to confirm that the raw command (hexidecimal?) being sent by the C+ is indeed the command that will perform the intended action on the HX Stomp.
I was able to send a MIDI command from the computer to the HX Stomp without issue, which tells me that this is a communication problem specific to these two devices. Since the C+ works with the Ampero Mini perfectly, I am still inclined to believe the fault lies with the HX Stomp.
After discovering the above, I downgraded the HX Stomp firmware to 3.71 to see if this was perhaps a bug introduced by 3.80, it did not have any apparent effect.
Attempted to use a USB hub (knowing it was certainly not going to help, but I'm at my wits end)
Changed the way the command is sent (Single step, short press, long press, etc)