The in-ceiling budget will probably work if you figure on ~$200 per pair for 6 pair of speakers plus 6 (~$50 apiece) impedance matching volume controls.
You will not be able to get 6 completely different zones, each playing a different source, for anywhere near $1K. For under $500 you could get a receiver with zone 2 capability and have the main room play a different source than the other rooms, but the other rooms will essentially be one zone and all play the same source (though different than the main room).
That doesn't leave much money for speakers in the main room.