I think it will be really tough to do what you want on a $4000.00 budget.
The biggest problem is those ceiling speakers.
The cheapest way of doing this is to get a distribution amp, say from Russound and put impedance matching volume controls in each room. So you would connect the receiver zone 2 to the ditriution amp and buy one big enough to have enough amps to supply each room. You would be able to control the volume in each room manually, but not remotely.
If you want remote control in each zone, then probably the Sonos Port is your best bet.
In this case you would need a Sonos port connected to an amp for each room. You would connect the ports to the zone out on your receiver, and each port to the room amp. This is going to bust your budget mightily.
At this time I should point out that wired speaker systems are out of fashion.
My feeling is that it would be simpler and cheaper to ditch your wired ceiling speaker syteem. These house audio systems are now going wireless. So you should take a close look at Amazon Alexa and the Sonos sytem espeically.
One of my sons has the Sonos Connect system which the Sonos Port has replaced. He also has wireless Sonos in some rooms. My impression is that the wireless works far better then the wired. I have no experience with the Port, but Sonos claim improvement.
Your TV does not have HDMI ARC return which complicates issues. So you will have to use the optical SPDIF out connection to the receiver to hear streaming apps from your TV. This will work about as well as the 2K TVs ARC return.
The newer 4K TVs have much improved ARC return. It is much more full proof and supports loss less audio. Basically it is how this should have worked from the beginning. It is now excellent, and actually probably one of the best reasons to upgrade to a 4K TV.
The TV room is actually going to be the easier problem to engineer.
So you need to know how large you can tolerate the speakers and sub. With speakers it is very much the bigger the better to a certain point. If aesthetics are a big issue, you should consider in wall speakers. Here is a link to a
DIY in wall speaker system I built and installed in one of the rooms of our new home.
I would start looking at receivers from Yamaha, Denon, Marantz, and Sony to see what you think miight be suitable for you.
I have the feeling you may not be experienced, just a hunch though. This system, because of the associated in ceiling speakers and your desire for remote control, it might be wise to engage a dealer, or installer who is also an integrator.
Things are very different now, from the time you installed that Bose system.