I really like that idea about the Fighting Hearts -- especially the higher ups of them -- having the shards of The Conerstone of Light as necklaces. It would be a good reminder of what their fighting for.  

As for the Fighting Hearts traveling, they're doing it via Gummy Ship. Your point about it being monitored by The Empire is a good one, but we can easily make the case that the Gummy Ship that they use is a special brand that is totally concealed from the Empire's ships systems.