System building advice needed

Hey gang,

I could use some help finding the right device(s) to meet our criteria.

I've just ordered Polk R600s that I'll be using as my front stereo pair.  These will go at the front of our 16' x 35' great room where we spend most of our time.  My primary listening seat on the couch is about 9' away, though I will also listen standing and further back.  The Polks are only 87.5dB sensitive, 4 ohm, and need some decent power.  

At the back of our great room is our kitchen.  My wife has asked for a solution that will allow her to hear tv programs from back in the kitchen, without having to turn up the speakers so high.  In this scenario she is nearly 30' from the main speakers.  For this I've ordered a pair of Polk R900s which will hang on the wall above our cupboards.  

Consequently I need to find the a good solution that will allow me to power both sets of speakers (and send the same "front" signal to both pairs).  I also need it to have a subwoofer out, and some form of tone controls or EQ (for the R600s that will be very tight to the front wall).  Dirac would be amazing but not required.  Bluetooth or streaming capabilities are a nice bonus also.  Biggest priority however should be on sound quality for the R600s.  My bias is against buying a receiver, but I'm open minded.  Connected sources will be mostly digital (toslink or Hdmi) and we mostly stream our music.

Budget is ideally under $2K, and I am open to new or used gear.  

Thanks!