I ended up changing this to be a GameInstance subsystem instead. On the game side I wanted to access game settings in the TTS factory, and Engine subsystems were too early to handle that.
By making this a game instance subsystem I was able to ensure the modules are loaded first, that I can use the Collection.InitializeDependency to ensure subsystem ordering, and am able to access the data I require in my factory for TTS. Having my subsystem be GameInstance and the SlateScreenReader one be EngineSubsystem would sometimes initialize out of order in some builds, and I didn’t have a good tool to fix that ordering (aside from maybe LoadPhase).