I think if you want simple you need to buy from manufacturers who specialize in multi room audio distribution, like Sonos and Russound.
So now you have the equipment you have a problem. I do not know of a six channel preamp that can control three stereo pairs. There may be one, but I don't know of it.
I don't know what quality you are after, but if this is a background/ceiling system I would add a remote controlled impedance matching speaker selector, and impedance matching volume controls in each room.
If it is high quality stereo you want in each room, then the way to go is to put discrete systems in each room and NO central control.
I personally hate background ceiling systems. I had no luck going the central route with remote speakers, and so for quality which I demand, it requires discrete systems in each space.
I know you realize this now, but you did not do your home work and investigation before purchase.