The Sherbourn has three composite video outputs and a second HDMI output that replicates the main zone. I would assume you want the highest possible quality level. Ideally what you would want is a 4x4 HDMI matrix switch (assuming you have 4 or less AV sources) - all of your sources go to it first, then the four outputs go to each zone location, including one going to your theater preamp "zone" which then passes that along to the projector. So that would get you HD video via HDMI to each location. But to get the audio into any type of in-ceiling speakers, you have a couple of options. One is to run the analog audio from your sources to the receiver and then take the receiver's analog outputs to a separate multi-channel amplifier. Another option is to get a dedicated multi-zoom source component that integrates everything in one chassis, but at a price. An example of this would be a Niles Multi-zone controller: http://www.nilesaudio.com/product.php?prodID=ZR-4%20SERIES2&recordID=ZR-4%20Multizone%20Kit&categoryID=Multizone%20Products&catcdID=2&prdcdID=FG01610
This kit also gives you programmable keypads for easy local control in that zone for basic functions, plus an integrated tuner and amplification. They also make a six zone, fyi. The last option would be to run the HDMI to each zone and then take the analog audio output from the TV in that zone and feed it into a local system (i.e. receiver, amp, etc.) that will power the zone speakers.
My own personal system will be a 14 zone multi-zone system with a common equipment rack and one of the more advanced home automation systems (i.e. Savant) so everything is distributed. Using a multi-zone receiver is easy if you can live with composite (non HD) video for the video source to remote zones. With your budget, there are no HDMI zone outputs I am aware of beyond just one extra zone.
I guess I'll have to wait on that steak and beer!