I think the POD has to be before the Shimabara Rebellion. I see three possibilities.
1) Japan's period of warring states is prolonged allowing more missionary activity before a Shogun can impose any anit-Christian edits.
2) The Shogun that units the control is either Christian or favorable to Christianity. Oda Nobunaga was supposedly favorable to the Jesuits, although it's hard to know what his position would be had he lived to unite Japan.
3) The Catholic Church better handles the position of the Jesuits in Japan with the desire of the mendicant orders to preach. Since the Jesuits were seen as being Portuguege and the mendicants Spanish, there is a political struggle here. But perhaps something could be worked out that would improve the Catholic position in Japan while not spooking the Japanese that they might become pawns to the Europeans. That might change some attitudes enough so that Hideyoshi or Tokugawa are less severe.
There needs to be a longer period of Catholics allowed to proselytize so that 1) a critical mass of Catholics is reached that would make it hard to crush, and 2) enough time so that Christianity becomes native and not seen as some dangerous form of foreignness.
Any Catholic majority in Kyushu implies correspondence with Rome, so in this scenario I can't see Japan becoming isolationist. In fact, it's likely Japan will continue to develop technology on par with Europe since it is in constant contact with it. Very different history here. And if Japan ever successfully invades Korea, or invades China with some initial success, it is likely to push China to reform far sooner than it did IOTL.