The files that I linked to are the exact, unaltered original MOD files that the Acorn Archimedes version used, albeit split into multiple files (since the true originals were combined into two files for each game, but were still in MOD format). Yes, even the instances where instruments seem to drop out briefly happen in the originals; that was done by the arranger to stay within a three-channel limit, which was necessary for technical reasons. (If you don't believe me, watch
this video, which shows gameplay of the first six levels. The sound quality isn't the best, but if you skip to
7:19, you can still tell that the example that you've given exists there too.)
If you still believe that those MOD files were somehow altered or ripped inaccurately, contact
ccexplore.
And please don't assume that the SPCs that you linked to are the originals. They're not; they're just some files that someone made for Super Mario World hackers who wish to use that music. And that version is definitely altered; many of those songs were extended and made to use more channels.
If you're interested in modifying the MOD files, you can open them in a "tracker" such as
OpenMPT. Note that all of those MODs have only four channels, so that's all that you'll see initially when you open them. To change a song's channel count in OpenMPT, go to the "General" tab and click "Song Properties". Near the top of the dialog box, you should see a drop-down menu that lets you choose how many channels you want.