I could be wrong, but maybe the last part of the Sweet Cap'n Cakes leitmotif part 1 is in Castle Funk..? I went to hooktheory to find the parts I thought matched, turned them into MIDIs in bandlab and got this:
The notes with a white outline are from Castle Funk, while the others are from Sound Studio. Also worth noting that the 6 notes have the same duration in both songs
The timestamp for the melody in Sound Studio is around 0:06-0:08 while for Castle Funk I think it's around 1:20-1:22 (but appears more throughout the song as well)
I'm putting the bandlab MP3 file of both melodies in quick succession:
Again, not sure if it will count, but I think it's a cool thing :D
EDIT: the 1st melody in the MP3 is from Sound Studio, and the 2nd from Castle Funk
I think this is highly possible.
My only gripe is that it comes from a very small and specific part of sound studio
butttt it DOES make sense for it to be there
and it DOES sound similar
so I'd say probably!