Your diagrams make the situation much clearer now. So the inaccuracies don't happen only at low levels but are rather distributed over the whole level range. On my DG4000, I counted seven attenuator relay switchovers, resulting in eight level bands within which the level has to be adjusted digitally by scaling the DAC input values. The ranges on my AWG are (all in dBm into 50 Ohms load, 1dB steps):
-56...-41
-40...-33
-32...-23
-22...-13
-12...-3
-2...+10
+11...+14
+15...+23
Since there are more than seven discontinuities in your figures (seems rather like eight positive and seven negative "errors"), my take would be that it's not related to the attenuator chain but rather to the digital signal path from the FPGA to the DAC. A problem like this should also result in some distortion of the signal. Did you look at the AWG's output signal in the frequency domain (FFT)? The problem may be related to something as simple as a defective BGA solder joint (hard to repair , depending to your available equipment and experience...). You may try applying some "tender pressure" to the FPGA and DAC casings to check for a change and maybe identify the problematic component. If it's an internal fault in one of these two chips (or maybe even someting sample-memory-related), things will quickly get pretty awkward.
For diagnosing these problems, a ramp waveform may be better suited due to the repetitive, periodic changes of the data lines. But sure enough, this won't be an easy job.
I don't think it's neccessary to move this "hijack attempt" to a new thread. Contribution frequency on this topic has died down since a long time so a few half-way OT posts won't do much harm, in contrary, it may help keep the information on this particular instrument in one place.