Is it prescribed to supplicate for the deceased in the second takbir after invoking blessings upon the Prophet, peace and blessings be upon him, if the Imam delays the third takbir?

If the Imam is slow in sending blessings upon the Prophet (peace be upon him), it is legislated for the congregant to supplicate for the deceased, because the purpose of the funeral prayer is intercession and supplication for the deceased. Al-Haytami said: "If the congregant finishes Al-Fatiha after the first [takbir] before the Imam pronounces the next takbir, then he should engage in supplication... And if he finishes sending blessings upon the Prophet (peace be upon him) before the Imam pronounces the next takbir, he should engage in supplication."