Making One's Chometz Hefker

Rashi on 4b in Pesachim d"h B'Bitul says that Bittul Chometz is learnt from a gezairas hakasuv of tashbisu. The Ktzos in Siman 273:1 asks, why could Rashi not learn like Tosafos that the bittul chometz works mitaam hefker?

The Ktzos uses a yesod that he uses in a number of other areas that perhaps hefker doesn't work as a "daas makneh", but rather mitaam neder. The idea is that one is not being makneh the item to hefker, but rather is making a neder that he no longer will be using the item. Thus, the Ktzos suggests that even if one were to make the chometz hefker, one would still transgress on baal yeraeh and bal yimatzei. Another place where the Ktzos discusses this yesod is in Siman 211:4.

Interestingly, the Ramban in the beginning of Meseches Pesachim suggests a possibility as well that hefker may not work to avoid the issur of baal yeraeh and baal yimatzei. Again, the same question arises, if the chometz is hefker (and thus not yours), why would you transgress the issur of owning it?

I once heard another answer to this question based on the words of Rav Soloveitchik. The gemara says that chometz is one of the items that isn't really in your reshus on Pesach, but the Torah places it into your reshus to make you transgress the issur (if you didn't properly do bittul or dispose of it). This is referred to in the gemara as "asaan hakasuv k'ilu hu birshuso". One possible explanation of this is that in dinei mamonos the torah places it into your reshus, causing you to transgress the issur. However, another way to explain is that despite the fact that the chometz isn't yours b'dinei mamonos, you still transgress as long as you were "rotzeh b'kiyumo" (you wanted it around) and you weren't "mechazer ulav l'sorfo" (you weren't actively trying to destroy it). This would then be another approach to answer the Ktzos' question. It's not that hefker doesn't remove the chometz from your possession. Rather, despite the fact that it does, it still may not work to remove the issur of baal yeraeh and baal yimatzei.