Praise be to Allah.

Firstly:

Singling out a specific time for remembering Allah, or praying for forgiveness, or sending blessings upon the Prophet (blessings and peace of Allah be upon him) falls into two categories: 

1.When it is done by way of worship and believing that there is virtue in doing this act of worship at this time. This is not prescribed except in cases where it is proven that this time is singled out by the Lawgiver.

2.When it is not done by way of worship; rather that time is singled out because it is a time when the person is free and has energy, and so on. There is nothing wrong with that.

Please see the answer to question no. 148174

Secondly: 

Before Fajr, i.e., before dawn, is a time when it is prescribed to pray for forgiveness, as Allah, may He be exalted, says (interpretation of the meaning):

“And in the hours before dawn, they were (found) asking (Allah) for forgiveness” [adh-Dhaariyaat 51:18].

 As-Sa‘di (may Allah have mercy on him) said:

“And in the hours before dawn”, which is just before dawn

“they were (found) asking (Allah) for forgiveness”. So they made their prayer last until the time just before dawn, then they sat, concluding their night-time worship (qiyaam al-layl) by asking Allah, may He be exalted, for forgiveness, in the manner of a sinner seeking forgiveness for his sins. There is a special virtue in praying for forgiveness in the time before dawn that is not present at any other time, as Allah, may He be exalted, says describing the people of faith and obedience (interpretation of the meaning): “and those who pray and beg Allah’s Pardon in the last hours of the night” [Aal ‘Imraan 3:17]. 

End quote from Tafseer as-Sa‘di (p. 809). 

Based on that, singling out this time for praying for forgiveness, as opposed to other du‘aa’ (supplication) and adhkaar (remembrance of Allah), is a virtuous deed that is prescribed in Islam, and if that is done whilst praying at that time, that is preferable. Ibn Katheer (may Allah have mercy on him) said: If the plea for forgiveness is made in a prayer (salaah – formal prayer), that is better. 

End quote from Tafseer Ibn Katheer (7/390). 

Moreover, it does not seem to us that there is anything wrong with sticking to the format mentioned with regard to asking for forgiveness: “Allahumma anta rabbiy laa ilaaha illa anta (O Allah, You are my Lord, there is no god but you)…”, as it is proven in the Sunnah that this is a good format, known as “sayyid al-istighfaar (the best of prayers for forgiveness).” But if you alternate between that and other wordings of prayers for forgiveness that have been narrated in the Sunnah, that is preferable and is better. 

Please see the answers to questions no. 126934 and 122968 

Thirdly: 

Abu Dawood (1047) narrated that Aws ibn Aws said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “One of the best of your days is Friday. On it Adam was created and on it he died; on it the Trumpet will be blown and on it all creatures will swoon. So send many blessings upon me on that day, for your salutations will be presented to me.” They said: O Messenger of Allah, how will our salutations be presented to you when you have turned to dust? He said: “Verily Allah, may He be glorified and exalted, has prohibited the earth to consume the bodies of the Prophets.” Classed as saheeh by al-Albaani in Saheeh Abi Dawood. 

Ibn ‘Allaan (may Allah have mercy on him) said: 

“So send many blessings upon me on that day” i.e., so as to increase it in reward and virtue, because a righteous deed is honoured by the honour of the time and place in which it is done.

End quote from Daleel al-Faaliheen (6/627) 

Al-Bayhaqi (5994) narrated that Anas said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Send many blessings upon me on Friday and the night before Friday, for whoever sends blessings upon me once, Allah will send blessings upon him tenfold.” Classed as hasan by al-Albaani in as-Saheehah (1407). 

The scholars of the Standing Committee said:

Sending blessings upon the Prophet (blessings and peace of Allah be upon him) is mustahabb (recommended) at all times, and is particularly emphasised on Fridays, without singling out a specific time for that.

End quote from Fataawa al-Lajnah ad-Daa’imah (24/162). 

Based on that, sending many blessings upon the Prophet (blessings and peace of Allah be upon him) on Friday and the night before is a virtuous deed that is prescribed in Islam, and it is proven in the Sunnah that it is recommended. 

With regard to as-salaah al-Ibraaheemiyyah, it is the best format for sending blessings upon the Prophet (blessings and peace of Allah be upon him), so choosing it for the virtuous time is a good deed that is prescribed in Islam, and there is nothing wrong with that, in sha Allah.

Please see the answer to question no. 88102

And Allah knows best.