Thanks Gareth, but after much searching around and realising that our "Active" and "Inactive" are Categories rather than inbuilt Moodle methods, I've eventually figured out that the lack of Summary and different rendering comes from the "Courses with summaries limit"; when viewing in Categories, if you have more than a prescribed number of courses then it reverts to a simplified display. Bump up the figure, and hey-presto!
That said, I just realised that you are primarily pointing me to where is a good place to make the changes for enacting the self-nomination icon. Thanks, now that I've got the other bit sorted I can start looking into the meat of this one.