The JP2C is MIDI capable, so you can just set it up as a Generic CC/PC device. The simplest way to control it is to send PC messages to it. In the JP2C manual, there's a chart showing the default settings for each program change. For example PC1 is CH1 with all switches off, PC2 is CH1 + EQ1, PC3 is CH1 + EQ2, etc. You can send the desired PC to the amp based on this chart.
You can also set it u with IA buttons and CC messages. For now, you'll have to do this manually, looking up program numbers in the manual, but in the next firmware release, I'll have built-in support for the JP2C.