I've got some good options for his canter that really seem to match his rhythm in canter:
*I know that lyrics can be frowned upon in the ring, but perhaps instrumental versions are available out there?*
Elton John's version of I Just Can't Wait To Be King:
For his trot?
William Tell Overture (ending, Lone Ranger part)
I know the songs don't match each other, but throwing a few out that do seem to match his rhythm in the videos. I was tinkering with music from The Lion King; Elton John's versions of I Just Can't Wait to be King
for canter, Circle of Life
for trot (EJ version has more rhythm than the movie version), and Can You Feel the Love Tonight
for walk. Its a lot of lyrics, though, and I'm not sure where to go about finding instrumentals for them.
I'll keep my ears open!