That solves the problem of keeping all the speakers in sync.

I did something similar with IP tech. I put all my MP3s on a SSD connected to a 3 W ARM SoC at home. The software stack is deefuzzer + icecast + a number of different players according to the device I'm using. A web UI to skip to the next song or to search a string and create a playlist with the result. I setup a few channels by genre. I'm listening to my radio right now. The advantage compared to a FM station is that I don't have to care about interference (I would be the bad guy) and I can listen to it wherever I am.