Without the actual Talmud in front of me, it is hard to speculate. But I think that you have to say that Rav Shach has some way of understanding R. Yehuda (of the Mishna) in a different way than he is usually understood. R. Yehuda says ביעור חמץ the destruction of leaven is by fire. The way this is usually understood is based on a statement במה דברים אמורים קודם זמן איסורו אבל אחר זמן איסורו השבתתו בכל דבר. [When do we say this? Before the time it is forbidden. But after that time one can get rid of the leaven in any shape or form.]  Now based on a later on sugia [treatment of this subject] around page 93-95 in Pesachim it says leaven shall not be found is a prohibition that is transferred to a positive command. {לאו הניתק לעשה/a negative command that even if one transgress it he does not get lashes because it can be rectified by a positive command }That can only work if ביעור חמץ is only at the time of the prohibition. So to whom is that Gemara referring to? Apparently R. Yehuda.
This would at least help to understand the Rambam who does hold that ביעור is only at the time of the prohibition  and yet he gets lashes [because obviously he is going like the sages against R Yehuda] But the thing you see in the Rambam is the way he understood the argument between the sages and R. Yehuda--is what is the destruction of leaven? Anyway possible or only by fire? But both hold it is at the time of the prohibition. So this is how Rav Shach understands the Rambam and I think he must be basing it on that later Gemara.
Of course, none of this is like Rashi or Tosphot. And that leaves us with the obvious question what do Rashi and Tosphot do with that Gemara on page 93-95?

In any case there is clearly a lot of work that needs to be done here. Reb Chaim Soloveitchik also deals with this same question but I do not have his book nor the Gemara. At any rate his answer, is that לא יראה ולא ימצא is a positive and negative command--so that is how he answers for the Rambam which does not help us about the Gemara on 95.

In case it is unclear what I am saying here it is this. You can not have  לאו הניתק לעשה when the עשה starts before the לאו. They have to start and end at the same time for this law to apply.