What you are describing that you want is a centralized distributed system, and it may require a lot more equipment than what you have listed. An A/V receiver will handle a single surround area. Better ones can send out HDMI to a second TV or a second receiver, but that's as far as they go. They don't really handle duties for more than a few zones and start getting complex in their setups.
You have described needing FOUR outputs for video alone, along with another area just for audio. I would ask first, is that really it? Do you really only want one additional zone of stereo audio beyond the four TVs? If building, I would take this rare opportunity to put speakers everywhere you could dream of, or at least wiring for such. I recently retroed a home with 14 audio zones. Only two of them have TVs, but the dining room, living room, garage, master bathroom, and other areas were added for music during parties. That wiring was over half the labor involved in the installation due to the complexity of retro fitting wires into the home. It would have taken 1/4 the time had the home been new construction wiring.
That said, you will need a HDMI matrix switcher, and the quality falls right in line with what you pay. Monoprice HDMI matrix switchers suck. I've seen other ones which are not much better. The best ones carry a hefty price tag. Expect to pay about $5,000 for a 8x8 HDMI matrix switcher.
That will get your video switched, and if it is a REALLY good switcher (even more $$$) then it will handle ensuring that HD audio is available to the surround zone while other areas receive analog audio. That's a huge HDMI issue.
The Roku does NOT have a secondary output for analog audio I believe, nor does the AppleTV. Those issues will need to be addressed. The best HDMI switcher I know of (Crestron) will actually de-embed HD audio, and scale it to 2-channel stereo audio for stereo zones. A lot more than $5,000 for that puppy, but it really does what you can imagine.
You will want to have multiple cat cables to all TVs in rooms, and if you want any local devices (Blu-ray, aux inputs), then you will want to pull extra cat cabling to them for off-network use (video, control, etc.).
You will also need some type of preamp for the audio switching and matrixing as well as amplifiers for the stereo zones.
That 14 zone setup I did used a 43 space rack with a rear mounted 16 port switch on it. The preference is to NEVER move your equpment rack but get it in a location where you can get behind it and sit down behind it to work on it. If you must have it on wheels, bring the cables in HIGH, leave about 20' of slack on every cable you bring into the rack, and dress them in properly so they can flow back and forth as the rack is moved without getting caught under it in any manner.
Your situation is not unique, but it is still pretty pricey to achieve what you are after. I have avoided the HDMI matrix at this point in favor of component video distribution. It works reliably and was a heck of a lot less expensive.