Am I accountable for anything regarding my raising my hands during the Takbir of the prostration of forgetfulness (sujud al-sahw al-ba’di), and for not recalling the reason for the forgetfulness in my intention, given that I don't remember the prayers in which this occurred?

Raising the hands is not required in the prostration of forgetfulness (sujud (definition) al-sahw). It is sunnah (definition) to perform iftirash in it, and then at-tawarruk until one says the taslim (definition). The two prostrations in terms of posture and remembrance are like the prostrations of prayer. The prostration of forgetfulness requires an intention concurrent with the takbir or slightly before it, and there is no need to recall the reason for the prostration. The previous prayers are valid and are not affected by not raising the hands. If a worshipper forgets the post-taslim prostration, he may perform it whenever he remembers, even after a long time.