Using two mono amplifiers to make one stereo amplifier
Such chips exist:

http://www.analog.com/media/en/technical-documentation/data-sheets/ADAU1373.pdf

There's one in every cellphone... however the real problem will be finding them in a package that isn't some microscopic variant of BGA.

Please note that I2S sends both channels on the data line, and the WCLK line distinguishes left and right channel. If you use 2 chips, like in your schematic, your chips need to be aware of this and be able to extract the proper channel from the I2S stream. The ones you quoted are able.


  The ShutDown/Mode pin can be used to put the chip in shutdown or set up which I2S audio channel is piped to the speaker. By default, the amp will output (L+R)/2 stereo mix into mono out. By adding a resistor, you can change it to be just left or just right output


I suggest using DigiKey search tool, search for codecs/dacs, with headphone amp in the features, and filter by package maybe.