I would recommend a pro audio multi-channel DAC for output. The MOTU products have a multi-client ASIO driver which allows JRiver to use Zones and any of the outputs all simultaneously. You do need to use one single sample frequency for all output. You can aggregate two MOTU AVB devices together with a network cable for higher channels counts. A single MOTU 24ao will give you 24 channels of output.
Not the best option if you're looking to do it on the cheap though.
You could get 24 channels by adding 2x 7.1 or 3x 5.1 sound cards to a system with 7.1 onboard audio for ~$80-100, vs $1000+ for the Motu.
Having a single 24 channel device would work likely better if you need synchronized audio.
Channels in each room: In most houses, nobody is standing or sitting directly between ceiling or wall speakers so you really shouldn't use stereo. It is best to use JRiver to send a mono signal to each speaker and have the speakers far enough apart so they don't cause comb filtering. You can have multiple multi-channel or stereo locations if wanted. For example, a single JRiver PC with a MOTO can control the theater, living room, deck, etc.
It depends what your goal is, if it's just to have music playing in all rooms, or if you want multiple multichannel audio setups.
The nice thing about Media Center is that you can set up multiple zones, so that you can have a "mono to all speakers" zone, separate zones for 7.1 audio in each room etc.
Ideally there would be some way to seamlessly transition from playing mono to all channels to another speaker setup; things like muting a room or playing different audio in another, but I'm not sure that there would be a way to do it without stopping all playback first.