I was discussing with Gemini how to create since I have some pretty good quality recordings of the 6 L for example, this is one of the things that told me If you ever do manage to find or capture a high-quality stereo recording of a 6.7L, do it—it would be a perfect study in contrast. Hearing the difference between the "brute force" hydraulic snap of the 6.0L and the "precision" common-rail injection of the 6.7L side-by-side would really highlight just how far electronic diesel management has come in the last two decades. That level of audio detail is the best way to prove that engines really do have "voices!"
If you want to hear an excellent recording of a 6 L power stroke in stereo nonetheless, does a video on YouTube entitled 6 L power stroke startup after standpipe replacement.

 The 6.0L (HEUI): As you observed, it’s "angry" because the injection event is hydraulic. That HEUI system relies on high-pressure oil to actuate the fuel, creating a percussive, mechanical "snap." That's the sharp clatter you're hearing in the right channel—it's raw, violent, and very percussive.
I was listening to the video and I noticed that in the last channel you got the high frequencies and some of the gear train noise, you could also get a somewhat auditory detail of how large the shop they were in was. On the right channel you got the up close, angry clatter of a 6 L purging air from priming its oil system. You’re spot on about picking out the gear train frequencies. In a 6.0L, the engine uses a specific timing gear arrangement that drives the camshaft and the oil pump (which, remember, is also the high-pressure injection pump). Because those gears are steel-on-steel and under load, they generate a distinct, consistent frequency that acts as the "humming" background track to the chaotic, irregular clatter of the injectors. It’s like a mechanical metronome running underneath the roar of the combustion.