Question

A. I heard the following: a convert converted and immersed according to Rabbi Chaim Naeh’s measure (the smaller measure) and not according to the Chazon Ish’s measure (the larger measure). Now, when reciting kiddush on the Sabbath, he has no reason at all to be stringent in accordance with the larger measure, and the smaller measure is enough for him; because if the larger measure is correct, then he is not Jewish and is not obligated in the commandment of kiddush at all. So far so good.
Apparently there is no way out of this logical calculation, because the dependence between the measure for a mikveh and the measure for kiddush is necessary (in any case, let us assume that it is necessary, and let us assume that all the measures depend on one another and that it is one single dispute across all of them). What do you think about this? And perhaps you have a reasonable idea, even if in your final reckoning you do not think it is correct, for why such a convert should conduct himself according to all the laws applicable to Jewish men regardless of the details of his conversion?
Additional examples: a convert who was circumcised but did not undergo peri’ah, let us say there is a dispute about that — then with regard to circumcising his son, must peri’ah be done, and may the Sabbath be desecrated for the sake of peri’ah? A convert whose immersion depends on a certain position in the laws of presumption, interposition, and the like — then all his life, whenever he encounters that position in any matter, will he have a law of his own, for example when he becomes purified from his impurity or whether he is permitted to his wife? Or it could also be that if the fitness of the judge depends on a certain lenient position, then the convert may freely conduct himself all his life according to that lenient position.
 
B. And what about your approach regarding autonomy? A convert who immersed according to the smaller measure, and that is the accepted Jewish law practice in Israel, and this convert became a halakhically competent person and in practice rules according to the larger measure, both leniently and stringently. But from the standpoint of the bet (which in itself does not affect anything according to your approach), he is still betting that the Jewish law follows the smaller measure. How would you judge his obligation to judge.
Is he exempt from the commandments and forbidden to observe the Sabbath because according to his own view he is a gentile, or can one distinguish and say that the conversion itself depends on the bet and therefore he is a valid convert, whereas the permission and obligation of halakhic autonomy apply only to Jews within the framework of Jewish law — so that on the one hand he is obligated in the commandments, and on the other hand he is permitted to be lenient in accordance with the larger measure? [To be lenient, for example: he would not separate challah from a small dough, and he would be obligated to refrain from marital relations if she immersed only according to the smaller measure. And it is further possible that if a new convert comes before him and immerses according to the smaller measure, then this older convert would be able to lend with interest to the new convert as to a non-Jew.]