I rely on getting aTournie for the last couple of days! It means you can save the low level battles for the required battles for the tasks and have a good chance of getting them straight away. My level 190 island usually has no problems with battles but my small island couldn't do them without the low level Tournie rounds. Even my 190 island has been know to get stuck on a Battle,type for several hours as we don't have a Diamond to fight it. No such issues with the first stages of a Tournie.
Good luck!