Solved!
I've figured out how to do this after some hair tearing. Example with a two channel MIDI instrument switching between two channel strips in Mainstage:
1. Switch to layout mode (top left corner)
2. Add two keyboards (Screen Controls Palette:Shelf Controls) to the layout
3. Click the first keyboard, and in the Screen Control Inspector choose the input device and the first of the MIDI channels you want to use. Name the instrument 'Instrument C1' (or something like that)
4. Click the second keyboard and choose the same device, but choose the second of the MIDI channels you want to use. Name the instrument 'Instrument C2' (or similar)
5. Switch back to edit mode (top left corner)
6. Select the first channel strip you want to use, and go to its MIDI Input tab
7. Under 'Keyboard' select 'Instrument C1'
8. Select the second channel strip and select 'Instrument C2'
This is extensible to an arbitrary number of channels (up to the number of MIDI channels your device supports).
It's a bit involved, but I can confirm that it does do the trick.