So I did some trawling through various library websites last night, and not only was I able to find copies of the Italian, French and English books in various languages (Swedish, Danish and German), but I was able to actually find what appears to be a new
nature method course, published by the same Naturmetodens Sproginstitut
. It seems to unfortunately only be in Denmark, but it's still worth a shot to go look at when the libraries reopen (sadly I think it'll be much harder to get a scan and I can't read Danish, so don't know if it'd be available to check-out from the library to be able to scan it).
I was unable to find anything about the Russian one, though, and it really seems like there's only vol 3 at MSU. Quite disappointing. I still might contact the Humbolt institute again, just in case someone else there might see it and know about the old courses. It'd be interesting to see their other ones too, even if lower quality (I believe they had Spanish, German, Turkish and maybe some others besides the Russian?)
Edit: Actually, I might have just found a link to a Spanish one?https://www.worldcat.org/title/amt-natu ... ef_results
It seems that they have English and French as well, with audio cassettes. I don't know if it's the same ones that eventually found their way to Humboldt, or the quality, or if it's even the same series but if there's someone in that area of Germany it might be worth looking at.
I've also found what appears to be a 'continuation course' for their English one. Whether it's a part 2 or just already part of the earlier one that's available online, I don't know.