All this time I thought the titular Purple Prince was Kabumpo, the Elegant Elephant and a staple in the court of Pumperdink. (Pumperdink is one of the little kingdoms in Oz.) I figured they'd made him a prince. But in the end it was Randy who was royalty: he was actually Randywell, Handywell, Brandenburg Bompadoo, Prince of the Purple Mountain and—by the end of the book—King of Regalia. (Regalia being another of the little kingdoms in Oz.)

In lieu of an actual review, here are some keywords I wrote down:
Randy
Kabumpo the Elegant Elephant
Faleero
Jinnicky the Red Jinn
Kingdom of Regalia
River Road
Torpedomen
Stair Way
Nandywog and Tripedalians
Guide Post Man
Red Looking Glasses
Double-Ups
Ozwoz the Wonderful Wozard
Johnwan
Competitiveness between Wizard and Red Jinn
Cameo appearance by Ozma