The Learner/Burner Question -- part 1

Introduction:
Towards the beginning of Bavli Pesachim (7a), there is an underappreciated brayta which reads:

היה יושב בבית המדרש ונזכר שיש חמץ בתוך ביתו מבטלו בלבו אחד שבת ואחד יום טוב

Since this brayta is cited in the context of a discussion of whether it is possible to nullify chametz once the onset of the prohibition has arrived, and the brayta is analyzed and reinterpreted in the gemara in this light, it is easy to overlook the primary message of this brayta.

The brayta states that if one is sitting in the study hall learning Torah and then recalls that he has chametz in his house, he should nullify it in his heart rather than leaving the study hall and destroying it physically. Furthermore, one might think that this nullification has the status of kinyan, a formal acquisition and transfer of ownership, which is forbidden by Rabbinic decree on Shabbat and Yom Tov lest one come to write. Therefore, the brayta informs us that for whatever reason¹ one may perform this nullification on Shabbat and Yom Tov ab initio, and that it is effective.

(footnote 1: perhaps that it is not considered an acquisition, and is different from hefker, or perhaps because it is an acquisition that does not involve an act)

The first of these two novel points, that Torah study supercedes actual performance of a commandment to remove chametz from one's house, seems at odds with other Tannaitic sources which imply or explicitly state that the removal of chametz takes priority. In this article, we shall demonstrate and consider this contradiction, and will propose two approaches to resolving the contradiction. Further, we will demonstrate the surprising fact at these two approaches are actually put forth by Amoraim. Additionally, we will discuss this brayta in great depth from a traditional and academic perspective, in order to highlight specific salient aspects of the brayta.