I believe at 16:34 a different song starts that we also don't have. They seem to be in different keys (first in F major, second in Bb major) but that could just mean that its a different section of the same song, so it doesn't completely rule out them being the same. Luckily for our search, I think the first song starts with that clarinet descending motif, so we should only have to listen to the first second or so of anything to determine if it's correct.
Been searching this morning. I went through the full discography of the Original Alpenoberkrainer on Spotify and have looked at the available albums for the group between 1980 and 1987 on this account. No luck so far.
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