I am not perfect....I always need to say this since the year 2002........till today those words are still valid... but in this case I can help you only a little bit:
In the Zip file, in the sound sample "wegotbee3.wav" I can hear the track "Happy Sixties" from the Composers Stephane Huguenin, Yves Sanna & Christian Padovan.
It is from Focus music, from the Album "KOS 73 - Happy Sixties - Volume 1"
After looking into it, I think the version used is "Happy Sixties Remix" from KOS-151, but a huge thanks to you for this info.
I'm guessing that some of these might actually be short musical stings created for those episodes specifically, namely the "Bang the Drum Timely" rimshots and the solo piano "Row Row Row Your Boat" from "Hen and Bappy".
That "Penny Hearts Joey" bass gliss might be a sound effect, I'm guessing it may be on the Cartoon Express library since that has a ton of short musical effects, or even on the ProjectSAM "Animator" library.
I feel like the rimshots might be original, or they were sourced from somewhere, especially given that the episode ends with the drum part of "Stand-Up Comic B" before cutting to the cymbal crash of "Drum Rolls (a)."
I've listened through all the bass glisses from Cartoon Express on SourceAudio, didn't hear anything that matched. ProjectSAM is a possibility given the show's usage of Symphonic Adventures, but I've yet to see the contents of ProjectSAM Animator show up anywhere.
A big problem with ID'ing a lot of these is the lack of cue sheets and/or available info. I've checked GEMA, and the only entry they have is for "So Happy Together/Sweet Sixteenth," and I don't know any other website like GEMA with cue sheets.