Is it permissible for someone who doubts during the last Tashahhud, while saying "Bless Muhammad," to complete the Tashahhud and then repeat it as a precaution before the prostration of forgetfulness (sujud as-sahw)?

What you did by returning to invoke blessings upon the Prophet, peace and blessings be upon him, when you doubted whether you had done so, was the correct action. This is because the default assumption is that something doubted has not been performed. Your prostration of forgetfulness (sujud (definition) al-sahw) in this situation was not obligatory, because you performed a prescribed remembrance in an improper place. This does not invalidate the prayer intentionally, and therefore, sujud al-sahw is not required for it.