I finally decided to check which exact versions of the Doom I music lumps these MIDIs correspond to. There are 3 "revisions" of the MUS lumps, the first ones are used in versions 1.0-1.25, the second revisions in 1.4-1.6 and the final revisions in 1.666-1.9. For Doom II the story is much simpler as there is only a single version of the MUS lumps used in all versions (1.666-1.9). I am not sure what, if any, audible differences there are between these versions. In each of these revisions, most of the MUS lumps were changed/updated.
Converting the Doom I MIDI files through the official MIDI2MUS yielded a byte-for-byte match for the lumps used in versions 1.4-1.6 so these are not apparently the very final MIDI files. This is interesting also because the music lumps for the registered episode music of this specific revision were not previously available since those releases were shareware only. The reason why it matches this revision is perhaps because there is also an earlier OS/2 build out there that matches Doom version 1.6 and the Doom I MIDI files were never updated.
Perhaps unsurprisingly, all the Doom II MIDI files yielded byte-for-byte identical matches to the MUS lumps.
As a curious side note, the single Doom I MIDI file included in Doom95 matches the 1.666-1.9 MUS lump when converted with MIDI2MUS, thus it seems to be a later final revision of the MIDI. The MIDI files that used to be available at bpmusic.com did not match any lumps.