Is the opening Takbeer (Takbeerat Al-Ihram) required for the prostration of forgetfulness (sujood as-sahw) that occurs after the salutation (tasleem) from prayer?

What you are doing by saying "Allahu Akbar" for the opening takbir for the prostration of forgetfulness (sujud al-sahw) and then saying "Allahu Akbar" for the prostration is a mistake. The prostration of forgetfulness, if performed after the taslim, is not an independent prayer; rather, it is a rectification for the prayer and subordinate to it. The Sunnah is for the worshipper to say one takbir and then prostrate, then rise saying "Allahu Akbar," then prostrate again saying "Allahu Akbar," then rise saying "Allahu Akbar," and then say the taslim, just as the Prophet, peace and blessings be upon him, did in the story of Dhul-Yadain.