Check out the Marantz M-CR510 Wireless Network Receiver.  It is 11.8" deep and has most of the features you requested above.  It is new and I have not heard it.  That being said, Marantz has a reputation for producing very good equipment and is reasonably priced at $599.  I personally like Marantz a bit better than the Onkyo/Integra equipment so this might be a modest step forward in sound. 

Another option I founds for you was the Arcam A19.  It is on 10.8" deep. It is $999 and is a great sounding integrated.  The issue is, it has none of the network integration that you are looking for.  Integrated Amps typically don't have wireless and networking features as those are typically features of a receiver.  For Spotify and Pandora, a  Network Player which is effectively a DAC with the internet based features of a receiver, would meet your needs.  The Cambridge Audio Sonata NP30 would work and is $599.  There are a few others.  NAD, Pioneer Elite, Musical Fidelity and a bunch of other manufacturers make them.  Just double check the features and make sure that the services you want are available. 

The Marantz, Arcam and Cambridge units above are available at AudioAdvisor. 

If those don't work, you can churn and burn through specs at a few sites - Crutchfield, OneCall, AudioAdvisor (mentioned above), MusicDirect & Needledoctor are all good websites with good slections.  Search on integrated amps and look at the specs and all of them carry network players as well.  Each of those three retailers also offers a 30 day return policy.

Good luck and I hope this helps. 

I suggest that you get the NAD C326BEE amplifier, which is 11 inches deep.

That will give you plenty of room at the rear for cable connections.

It is a very good amp.

The Audioengine D1 DAC is only $169, and is very small and can be placed almost anywhere.