I read that if you recite Darood 1,000 times daily, you won't die without getting the glad news of Paradise. I have also seen Dhikr, for example, which says "praise be to Allah as many times as the number of His creations." Would it be correct, if someone wanted to send much Darood, to say "O Allah please send your prayers and blessings on Prophet Muhammad (Sallallahu Alaihi wa Sallam) one billion times" instead of repeating the Darood one billion times in one day.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

Invoking blessing on the Prophet (Sallallahu Alaihi wa Sallam) is a form of worship so the more you perform it the more reward you get. al-Tirmizi reported in his Sunan that Ubay Ibn Kaab said: 'O! Prophet (Sallallahu Alaihi wa Sallam) of Allah. I increasingly invoke blessings upon you. Would you tell me how much of my prayer should I devote to you. He (the Prophet (Sallallahu Alaihi wa Sallam)) said: "Whatever you wish". I said: 'the quarter'. He replied: "Whatever you wish and the more you do the better for you". I said: 'the half'. He replied: "Whatever you wish" . The Hadith goes until the Prophet (Sallallahu Alaihi wa Sallam) said to him: "Then, your worries will be dispelled (as a result of these invocations) and your sins be forgiven" . This Hadith is enough evidence that multiplying invocations upon the Prophet (Sallallahu Alaihi wa Sallam) brings a lot of good and a great reward.
However, specifying a given number and claiming that whoever performs it will not die before hearing glad tidings of entering Paradise has no evidence in Shariah. Specifying a reward for that or a given time for it is not mentioned in the source of evidence of Shariah. So all that is just soundless.
Finally, we advise anyone who likes to invoke blessings on the Prophet (Sallallahu Alaihi wa Sallam) to do that according to the forms revealed in Shariah as that is safer and more appropriate. However, although we believe that the forms revealed in Shariah are better, we do not see any objection to the repetitive formula mentioned in the question.
Allah knows best.