Upon further inspection, this short was apparently apart of a series of education shorts created by Hanna-Barbera from 1978-1980 called 'Hanna-Barbera Educational Filmstrips'. The short in question is most likely a segment in one of the shorts titled 'Healthy and Happy' which features the Banana Splits.
I personally am willing to join this hunt. I love the Banana Splits and would love to find these shorts. First of we need to contact the remaining alive voice actors for the characters, as there are different actors for voice and body, to see jf they remember it, then contact Marty and Sid Kroft to see if they have a copy, as they most likely consulted or wrote the scripts for the Banama Splits Shorts, then check with the WB archives to see if they have them, then work from there. Maybe find who else produced it and contact them.
Without archival, humanity would be lost to the sands of time.