Airpot Express - Upgrade amp or DAC?

Your problem is the AE, and no DAC will fix this. I know because I have modded the AE in the past for customers and developed several types of reclockers to make it sound good, including the Pace-Car and the Synchro-Mesh.

The Synchro-Mesh is the best way to make the AE sound good IME. What it does is reduce the clock jitter of the signal from the AE by establishing a new master clock. Jitter makes the audio diffuse and unfocused. The SM inserts between the AE and the DAC or SS receiver.

The digital source and the master clock inside that is the most important thing in any digital audio system.

BTW, the Sonos is another option to the AE. Most people use Sonos. It will not play hi-res but neither will the AE.

Steve N.
Empirical Audio

This is not accurate. DAC will improve AE since it has relatively low jitter on digital output but horrible jitter artifacts on analog out. You can find measurements here:

http://www.stereophile.com/digitalprocessors/505apple

Any jitter suppression, either by reclocker or upsampling (reclocking) DAC is always beneficial.

It sounds like you have done some critical comparisons already and have idenified a system weakness that you know can be improved. I would follow that lead and get a DAC that you know something about or have heard. The audition is always the single best advice you can get.