Is it permissible to perform six rak'ahs after the Duha prayer and six rak'ahs after the Sunnah of Dhuhr with the intention of absolute supererogatory prayer, and to persist in doing so daily in this manner, without believing in their specific Sunnah-status? Is this act permissible in Islamic law, or does it fall under the category of innovation (bid'ah)?

Prayer is the best subject. Absolute supererogatory prayer (nafl mutlaq) is permissible at all times, except during the prohibited times, and with any number of rak'ahs. However, one should not consistently perform absolute supererogatory prayers at a specific time. For this reason, scholars have mentioned that one should not consistently perform prescribed prayers that the Prophet, peace and blessings be upon him, did not consistently perform. Therefore, it is better to sometimes vary the number or the time.