What is correct concerning prayers in which a prostration of doubt was repeated without a takbir, taking into consideration following Imam Ahmad's view on the prostration of forgetfulness for unknowingly omitting wajib (obligatory) acts?

There is no need to repeat the prayers in which the takbirat al-intiqal (transitionary takbir) was omitted due to ignorance, because the takbirat al-intiqal is an obligatory act (wajib). Obligatory acts, according to the madhhab of Imam Ahmad, are waived due to ignorance or forgetfulness, and are compensated for by the prostration of forgetfulness (sujud al-sahw), which itself is waived if a long period of time has passed.