Using A & B speakers will get you nowhere, as they are supplied by the same power amps. So there is the possibility of having A & B speakers on together and a fried amp. Also you would only run two rooms in any case and not four.
What is your Yamaha receiver model number? I need to look at the manual. If the receiver were operated in five channel stereo mode, then you could run a room off the fronts and a room off the surrounds, and may be a room for zone 2 with a separate power amp. However on a lot of receivers only analog inputs appear at zone two, not the digital ones. That would still only give you three rooms and not four.
Quite honestly though your real solution is an impedance matching speaker selector switch.
This one is $34.99. For that little money I see little point in making this complicated. You just run your Yamaha in stereo mode and connected either A or B speakers, not both, to the impedance matching switch. Connect the speaker leads to the switcher, correctly set the impedance switch on the switcher and you are done! You have a safe installation.