GreenHopper gadgets give a 500 error when being configured in Confluence

To reproduce, add a gadget (for example, the hour burndown gadget) to Confluence.

When the necessary configuration is entered directly into the macro body, it works fine, so it's only the configuration step that is broken.

The Card View, Hour Burndown and Project Progress gadgets are affected.
Agile and Days Remaining gadgets are not affected.
I couldn't find the Cumulative flow and Statistics gadgets, so they should be assumed broken.