So, to get this to work I had to make a handler in the project's "Session Events" to receive from system.util.sendMessage(..., scope='S'). It then just calls system.perspective.sendMessage(..., scope='session') with the same payload. The component can receive this latter broadcast.
This is a nuance that should be put in the documentation. (That messages broadcast to Perspective via system.util.sendMessage(..., scope='S') can only be received in "Session Events".)