Ditch the iPhone as a source, your MAC/DAC deserves better. Get a Martin Logan Unison streamer with ARC room correction for $199 on sale. It has airplay. Use the iPhone as a controller streaming via airplay to the Unison. Run ARC room correction while connected to your DAC and you will be very happy.
I have this same setup with my Sony DAC and it wows. You can also use it with a sub if you have one.