I've never played that game...so I can't relate to everything you are saying about it... Have you tried the different modes you can start the game using (example: hit select on the main menu on the game you wanna change, and choose mode 1, 2, or 3. Or any combo of them.) Just a thought. Those compatiblilty sites aren't always correct, I installed Crazy Taxi directly to my HD via IDE and it plays fine, but the compatibilty sites say its incompatible. If not your just going to have to resort to playing Monster Rancher with your original.
Good luck.