The peak meter shows no overload, yet a dense recording sounds harsh. One possible cause is intersample peaks: the reconstructed waveform can rise above the individual sample values in the file.
What a conventional meter misses
Digital samples are not steps in a finished analogue waveform. Reconstruction and sample-rate conversion can produce higher peaks between them. Processing with insufficient headroom may clip those peaks. Sample-peak and true-peak meters can therefore report different values.
A practical check
Choose a short passage where the problem repeats. Reduce the player output by 4 dB before sending it to the DAC. This is diagnostic headroom, not a universal setting for every recording. Carefully restore the usual listening level with an analogue control after the DAC for comparison.
Control position matters
A control after an overloaded stage makes distortion quieter without undoing it. Even the DAC’s own digital volume control might operate after the problematic processing stage. Establish where attenuation actually takes place.
What this does not prove
An improvement does not isolate the cause: lower output might also prevent overloading a subsequent analogue input. Clipping already present in the recording remains. Measurements are needed for a firm diagnosis; harsh sound alone does not establish a faulty DAC.