Apologies for the out-of-order tracks everyone, I had left the numbers off the track titles because I thought that by changing the # on the files' properties, it'd be all ready to go. That was my mistake, and one I'll not repeat.
The sources of the following tracks have been identified so far:
Game Start - Inu no omawari-san
Main Theme - Araiguma Rascal
Frogger Homed 3 - Heidi, Girl of the Alps
Frogger Homed 4 - Hana no Ko Lunlun
Frogger Homed 13 & 14 - Yankee Doodle
Frogger Homed 15 - A Hundred Pipers
Restart - Camptown Races
If anyone recognizes the other tracks' sources, please don't hesitate to say something!