I know'd I shoulda checked it out first, but I so did wanna play with the howdy doody wordies. So, considering that our best efforts have avoided confronting the "howdah" explanation directly, I now have done my homework, and here's a definition from the Farlex Free Dictionary:
Urdu haudah, from Arabic hawdaj, litter, sedan chair, from hadaja, to shuffle along, totter; see hdg in Semitic roots.
Also, I shoulda remembered that it was the tiger that liked to climb the elephant's rump. Lions have too much dignity.