In this particular instance, I am working on converting Super Nintendo SPC music in to MIDI. The SPC format is somewhat similar to MIDI in terms of how it works, but does not have things like fixed pitch. The music is all sample based, and the pitch of notes is based off of the pitch of the sample. So if there was a piano, and the sample was recorded as an A, then the notes would be referenced to that A. The there may be another sound sampled as a D, and the pitch of those notes would also be referenced relative to the D. So the software makes a "guess" as to how those notes covert to a standard scale by running the sample through a filter and guessing based on the highest/most prominent frequency present in the results. There is no "standard" way that Super Nintendo games produced their sound. It was up to the individual game manufacturers to write their own sound engines. The SPC file format is actually a rip of the sound engine from the game, and then the MIDI-like note data that goes along with it.
I can sort of provide a sample, though this particular one doesn't seem to be that different volume-wise from what I've seen with some others. It may be as you say that in the game it is quieter to begin with.
https://www.zophar.net/music/nintendo-snes-spc/super-castlevania-iv Track #29 is the original ( the files are downloadable if you want to also download a player for them

)
scv4-22.mid - is converted with spc2midi, which has options for selecting instrument, volume, reverb, chorus, pitch bend, pitch (for correcting wrong pitch guesses), ADSR attack, and ADSR decay, and choosing whether a particular sound is instrument or percussion. Instrumentation was deduced/selected in the converter (still working on determining best GM1 instruments before I convert to GM2/XG/GS). This program was last modified in 2005. Strangely, if I disable pitch bend, the pitch actually changes by maybe 1/4 of a tone during playback. Not sure if this is the converter or the actual MIDI playback that is causing it.
Beginning_mod.mid - is converted with vgmtrans, which has NO options. Instrumentation was just quickly modified from its defaults with my instrument editor (MIDI-MIS!) to try to match the other one for demo purposes. vgmtrans is under current development, forked from an older project, but the MIDI output portion has not changed much in quite a while. One benefit of this program is that you can create a soundfont from the original game samples. Unfortunately, all instruments are assigned starting from 1 until the maximum sample number, with no way in the program to change which instruments they are mapped to, or adjust any other settings in the process.
It's a very time-consuming process to go through all of the files in the spc2midi MIDI converter to select instruments and figure out what sounds best for each. It wasn't until the past week or so that I realized I could adjust the pitch outside of their pre-defined -36 to +36, which is sorely needed in one particular game, where almost every track has different values for almost every instrument (one as low as -94!). Since I figured that out I've been much more happy with the results. It fixes some things where I thought the notes were all missing, when in reality they were either at much too high or low of an octave to be either audible or reproducible. I've been making an Excel spreadsheet so I have everything ready to go when I make the final files. I attached a partial screeshot.
My ultimate goal is to have the MIDI files sound as good as or better than the original source material. I am playing them back using the Timbres of Heaven soundfont as well as some others (like an 8-bit NES soundfont). I have at least 52 soundtracks that I regularly listen to, and I'd like to convert most of them.
De-quantizing sounds interesting, now at least I have a term that I can further investigate. This wasn't necessarily related to the video game music, just a general curiosity I had.