"Zwei Schimmel" and "Rote Schirme" no longer play in Oktoberfest (if they ever did). I am going to assume that either those songs never played, or they only played during a small window of time. In fact, the only songs by Alpenoberkrainer (on that list) that still play in the park today are: "Schöne Urlauszeit" and "Wenn der Opa mit der Oma tanzt."
The only remaining song in one that I have trouble finding with any music recognition apps. This song, performed by a Slovenian band, has the same chorus as the song missing from our playlist. The part we know starts at 0:30.