True MBTI type = True Socionics type. You're right that a J/P switch could work (and MBTI functions could therefore not be broken) if MBTI J = Dynamic and MBTI P = Static, but when reading all the MBTI introvert descriptions it never seems to be the case. This is especially noticeable in the ISXX descriptions but ALL introvert descriptions inherit more from the J/P dichotomy than they do from the (broken) functions.

To pass this off you would have to explain why MBTI J has a closer relationship with Dynamic than it does with Rationality, and why MBTI P has a closer relationship with Static than it does with Irrationality.