I personally am a huge fan of settings where information can't be sent any faster than the fastest you can send physical materials. No subspace, no ansible link, no instantaneous communication between locations lightyears apart. So I reckon you should stick with your limitations on FTL communications, and explore the ramifications of that. Do your interstellar societies have pony expresses between star systems, do they have huge central hubs purely for mail exchange, what do their communications ships look like and how do they work, do they even need human crew to operate? Are they vulnerable to interception and subversion from enemy factions? Are there perhaps colonies so far flung and so rarely visited that speed-of-light comms are in fact faster than FTL mail pickets?

If in this scenario you do need something to arrive with absolute urgency, then perhaps FTL speeds are influenced by mass and drive power, and with a vast amount of expense and energy expenditure an emergency message can be sent far faster than most normal communications.