90s (or earlier) novel: on a cut off colony after FTL travel wipes out life and becomes impossible, an emissary woman starts a college

I read this book maybe 15 to 30 years ago and my memory is hazy on this one. I cannot remember the title or author or describe if hard cover or not. The book was in English

Faster-than-light travel was discovered and used for many hundreds of years. However the stress on space-time by its use creates a storm that destroys most life in the galaxy. The destruction is centered on the space lanes, so whole life in the vicinity of Earth is wiped out. The furthest-flung colonies and beyond do survive. Only a few human outposts are left. Over the next few thousand years, some regain spaceflight, only use slow ships, and one by one the remaining colonies are re-found; raised up in technology so that they too can build ships and raise the other human colonies (a few hundred were left out of thousands).

The human race is in danger because aliens have also survived and astronomers can see the signs of millions of ships traveling below the speed of light on a journey of tens of thousands of years to, as people guess, make sure no humans can ever do that to the galaxy again. Humans think the aliens are themselves trying to survive a potential reuse of the faster-than-light drive, by preventing such technology from being used again, and the best way to do that is to wipe out all humans.

On one human slow ship going to uplift a colony, the crew traveled the long journey frozen in sleep. When they arrived at the planet, they studied the languages and cultures there, while not being observed, and then sent emissaries out to all the nations of the medieval-like world, to announce themselves and start a plan to raise the technology of the colony to their home planet’s own level over a couple hundred years. Not immediately, because as others found out the hard way, a sudden change of technology will often collapse the society and bring mass disaster. And they need an orderly change. This is where the story starts.

An emissary woman is the main protagonist of the book. She makes first contact with her host nation, and then gets involved in the very complicated politics and struggles that mark everyday life for the elite there. She starts a college, after getting permission for some of her slow ship crew members to come down and help, that introduces things like basic chemistry, math, and scientific thoughts. She fights in a few battles (unwillingly), and fails to save her friend, who dies in a first contact gone wrong in a neighboring nation state. Near the end of the story, discovering she had been manipulated by the local king for politics, she forces more concessions from him to make the college bigger and to allow more people from the slow ship down to teach his citizens .

She and a local poet become close. However due to the advanced medicine from her planet, she will outlive him by at least a hundred years. At the end of the story, he composes a poem that she thinks will be carried by his own people to the stars, as they will do their own uplifting of other colonies, starting two hundred years later.

I think the title of the book has something to do with that poem… it may or may not have the word "muse" in it.