That's very interesting kind of a sample cause the "unprocessed" sound (LHZ pedal in bypass mode) sounds as if there was PU resonance texture missing.
Ok, tried to do my my very best and did the following.
I downloaded the file from SC with JDownloader. The mp3 is of lowish 128kbit/s that I converted into WAV 44.1kHz.
I did split the file into two parts, the raw program material as part #1 and LHZ processed program material part #2
The raw program material part #1 was run into LT-Spice HAZ emulation with Treble and Bass at full boost.
In the next step I added a Pickup resonance emulation to the raw program material part #1 before the signal was again feed to the HAZ emulation in LT Spice.
raw program material part #1
- P-PU
program material part #2 processed by LHZ pedal
- P-PU_LHZ-pedal
HAZ LT-Spice emulation of part #1
- P-PU_LT-Spice
Pickup resonance emulation that was feed into HAZ LT-Spice emulation of part #1
- P-PU_LT-Spice_PU-Res
Conclusion
The LT-Spice emulation of the raw program material part #1 sounds a little bit boring vers. "real world" recording LHZ-pedal sound part #2.
Once there was some PU-resonance added to the raw program material before the signal was fed into the HAZ LT-Spice emulation the situation does change dramatically.
The emulated sound does come very close to the "real world" sound that was recorded with the LHZ-pedal.
The LHZ-pedal sound may sound a little bit more aggressiv at the top range of bandwidth vers. emulated sound. This remaining deviation might be aligned (at least at some content) with fine tuning by some variation of emulated pickup resonance and/or its peaking at resonance.
Yet I leave it as is. I did the emulation "on the fly" and to be honest, the emulated sound "as is" may sound (ironically) a little bit more pleasing to the ears than the recorded real world sound.
Download the PDF file "P-PU" and rename file extension "PDF" into "ZIP" to get access to the WAV files.
edit:
posts like this may read just as rant. Rather than rant those posts like this are rather meant to contribute to comprehension.
Me myself was very surprised that "adding" some missing pickup resonance may (strongly) help to achieve an intended sound goal. Interestingly it has nothing to do with shelf filters of the HAZ schematic in question nor anything to do with harmonics when digging in hard. Eventually it's nothing but a total different animal that contributes to the perceived "sonic" sound in question as is.