Another Missionary issue is that indigenous hostility to missionaries often lead to conflict with European powers. This was the immediate cause of much European territorial expansion. And even when it wasn't wars, especially in Asia.
France, and an avowedly anti clerical France at that, used it's self appointed role as protector of christians to involve itself not just in the Levant, but in the conquest of Cochin and the absorption of Indochina into the French Empire, it was used as a cassus belli with china on at least two occassions and also led to France being the chief European party interested in Korea, but by this point Japan was too strong.
And it wasn't just the French piety as a reason for conquest, the protection of "christianizing and civilizing" efforts was probably the largest source of popular approval for empire at home for colonizing powers.
Maybe missionaries if represented should represent not so much conversion but maybe some sort change of culture, because not all "missionary" activity was really religious in nature, but more involving modernisation. Japanese attempts (during game period no less) to begin transformation of the Taiwanese into devoted subjects of the Emperor for example involved such things as mandatory hygene classes, and a surprisingly large portion of missionary activity in the British Empire was the result of Catholic efforts, not protestant.