Well, I don't know the timings. But I've read Sulaiman (a) lived 712 years and started his rule at age of 12.
Well, there are traditions that Qaim's length of life will be the same as Noah:
Recorded in Bihar alanwar:
....Ibne Jubair that he said:
I heard the chief of worshipers, Ali Ibne Husain (a.s.) say, “There is a tradition from Nuh in the Qaim and that is the length of his life.”
Imam Sadiq said: “Allah, the Exalted, has consigned three qualities in the Qaim of
ours, which He had consigned to three of the apostles. He foreordained his
birth like the birth of Musa (a.s.);
his disappearance like the disappearance of
Isa (a.s.); and his longevity like the longevity of Nuh (a.s.). Moreover, He
made the lifespan of His virtuous servant Khizr a proof of his lifespan.”
There are some more Hadithes that says Qaim lifespan is like Noah, which was 950.
Now if the Qaim was born in 255AH, by now He must be 1190 years old, which contradicts the 950 years.
On the other hand, in the Hadithes it is said, Mahdi will be born during End Time. It is also said He will live 7 years after His rise:
"It is mentioned on the authority of Umme Salma that the Messenger of Allah (s.a.w.s.) said: “The Mahdi is from my Ahle Bayt from the progeny of
Fatima. He will act among the people according to the conduct of the Prophet.
He will remain seven years and then he will die and Muslims will pray over
him.”
"...the Messenger of Allah (s.a.w.s.) is the report of Abu Dawood and Tirmidhi from Abu Saeed Khudri that he said: I heard the Messenger of Allah (s.a.w.s.) say: “The Mahdi is from me. He has a broad forehead, a high nose that has a slight curve, and will fill the earth with equity and justice just as it will be replete with oppression and tyranny.
He will rule for seven years.”
Abu Saeed Khudri says: The Messenger of Allah (s.a.w.s.) said: “A man will rise from my Ahle Bayt and act upon my conduct. Allah will send down for him blessings from the heavens. The earth will bring forth its bliss. Through him the earth will be beset by equity and justice, as it will be replete with oppression and tyranny.
He will rule over this Ummah for seven years and will disembark at Jerusalem.”
This Hadith has been repeated many times.
Then there are Hadithes that says, the Qaim lives 120 years, like Abraham, such as this one:
عن أبي عبد الله قال:
القائم من ولدي يعمر عمر خليل الرحمن، يقوم في الناس وهو ابن ثلاثين سنة، ويلبث فيها أربعين سنة، يملا الارض قسطا وعدلا كما ملئت جورا وظلما
" القائم
من ولدي، يعمر عمر الخليل عشرين ومائة سنة يدري به، ثم يغيب غيبة في الدهر، ويظهر في صورة شب موفق ابن اثنين وثلاثين سنة، حتى ترجع عنه طائفة من الناس، يملا الارض قسطا وعدلا كما ملئت ظلما وجورا "
Now, there are at least 4 Hadithes I know, that says, the Qaim rules 309 years, such as this:
859 - (يملك القائم ثلاث مائة سنة، ويزداد تسعا كما لبث أهل الكهف في كهفهم.
The Qaim shall rule for 309 years, the same as People of Cave remained in their Cave.
I dont know how you would resolve these contradictions, But for me they are all clear. All of them match with established history and Scriptures of the Baha'i Faith.