Does the audible supererogatory prayer become invalid when performed audibly during prayers in which audibility is not prescribed, such as 'Asr and Dhuhr, for the purpose of reciting memorized portions aloud? And if this act is reprehensible (makrooh), is it a prohibitory reprehensibility (karahat tahrim)?

It is sunnah to recite silently in voluntary daytime prayers, by consensus. As for voluntary nighttime prayers other than Tarawih, one may recite audibly or moderately between audible and silent recitation. The regular sunnah prayers accompanying the obligatory prayers are all to be recited silently, by agreement of the jurists. The dislike for audible recitation in voluntary daytime prayers is a disliking of tanzih (discouragement) and not tahrim (prohibition), due to the differing opinions of the jurists on this matter. Therefore, reciting audibly in the regular sunnah prayers of Dhuhr and Asr is not forbidden, rather the disagreement lies in its disliking and permissibility.