TTS direct via skill is what could work, but I've only heard of one instance of a skill being able to announce from Echo without user input and they're canned responses, not user programmable. You could cast to a Google Home I suppose and you could send to a bluetooth or physically connected device that supported TTS, but that's not really what you're asking for and not really what I would want either.
I want TTS directly to my Echo in Alexa's voice. Not sure why it's not already possible, other than they might be concerned about abuse. Like your echo laughing at you in the middle of the night.