Did the Ruling Stewards of Gondor know where the Heir of Isildur was?
From the point of view of the books, there is no evidence to suggest that the Stewards had any idea that the Heirs of Isildur were alive or where they were. This seems to be supported by the confusion that Faramir/Boromir's dream gave them and the need to seek Elrond to solve it.
Seek for the Sword that was Broken,
In Imladris it dwells….
Fellowship of the Ring, Book 2
Furthermore, in Appendix A, it states that there were rumours of heirs in the North, but the stewards seemingly ignored those rumours.
...some remembered the ancient line of the North, which it was rumoured still lived on in the shadows. But against such thoughts the Ruling Stewards hardened their hearts...
Return of the King, Book 7: Appendix A
The films seem to suggest otherwise. From the line in the question, we seem to be led to believe that the Stewards of Gondor have a record of the heirs of Isildur, and that the current heir is named Aragorn, son of Arathorn. To what purpose this change has been made is unclear.
Why didn't the Ruling Stewards move forward to bring back the Heir.
From the books, they had no interest in doing so. Denethor was not the vain, bitter mad-man that the films portray him as, his rejection of an "Heir"'s claim was not of jealousy or pride, as is suggested by his humility in accepting that the line of Stewards will always remain Stewards:
"How many hundreds of years needs it to make a steward a king, if the king returns not? " he asked. "Few years, maybe, in other places of less royalty," my father answered. "In Gondor ten thousand years would not suffice."
Regardless of his humility, Denethor would have rejected any claim to the throne, as would any other Steward, most likely:
So! With the left hand thou wouldst use me for a little while as a shield against Mordor, and with the right bring up this Ranger of the North to supplant me.
But I say to thee, Gandalf Mithrandir, I will not be thy tool! ‘I am Steward of the House of Anárion. I will not step down to be the dotard chamberlain of an upstart. Even were his claim proved to me, still he comes but of the line of Isildur. I will not bow to such a one, last of a ragged house long bereft of lordship and dignity.’
Denethor clearly sees no value in the Rangers of the North and raising them up to the rights of a king. This was seen earlier in the histories of Gondor and Arnor when the line of the Kings of Gondor ended with Ondoher, at this time, however, the claim was rejected because of different laws of ascension between Gondor and Arnor and the way laws practised in Númenor.
The claim was rejected. In this Pelendur, the Steward of King Ondoher, played the chief part.
'The Council of Gondor answered: "The crown and royalty of Gondor belongs solely to the heirs of Meneldil, son of Anárion, to whom Isildur relinquished this realm. In Gondor this heritage is reckoned through the sons only; and we have not heard that the law is otherwise in Arnor."...
...'"Moreover, in Númenor of old the sceptre descended to the eldest child of the king, whether man or woman. It is true that the law has not been observed in the lands of exile ever troubled by war.
Return of the King, Book 7: Appendix A
The Ruling Stewards therefore both had no interest in rediscovering their King, didn't know if an heir existed and they didn't believe the line of Isildur were the rightful heirs, only the line of Anarion.
Why didn't the surviving heirs of Elendil return to Gondor earlier.
This is a bit of a confusing one, so I'll start with a little bit on the lines and then move down to why Aragorn was successful and why no one else really tried.
First things first. Elendil was High King of Gondor and Arnor after the fall of Númenor. After his death, his first son, Isildur was the heir of the High kingship and had all rights to the throne. However, Isildur was killed as he was returning to Arnor from Gondor, after committing rule of Gondor to Meneldir, son of Isildur's brother Anárion. After Isildur's death in the Gladden fields, Meneldir had assumed the Kingship of Gondor (while the Kingship of Arnor had gone to Isildur's fourth and last son, Valandil). It was henceforth that the rule was split between Gondor and Arnor, and from which the Stewards of Gondor claim the line of Gondorian kings comes from Anárion, who's line ended with Ondoher and his sons. The kingship of Gondor moved to Ondoher's (descendent) second cousin once removed, Eärnil II (Clear chart of relationship can be seen here)
Onto the first King of Arnor reclaiming the throne of Gondor. This occurred after the death of Onodher and his sons. Arvedui went to Gondor claiming the kingship as not only a descendent of Isildur, the rightful High King of Arnor and Gondor, but also as the husband of Fíriel, the rightful queen of Gondor according to the Numenorean laws of Ascension (detailed above). Arvedui's claim was rejected by a council of Gondor, by persuasion of the Steward Pelendur. Eärnil II was the raised to Kingship, however the line of Kings would end with his son, Eärnur in TA 2050, after defeating Angmar.
After Arvedui's attempts, he would go on to rule Arnor after his father's death, he would however be the Last King of Arnor as they were utterly defeated by the Witch-king and his armies our of Angmar. The people of Arnor would be scattered, wandering people, with Arvedui's sons taking the title of Chieftain of the Dúnedain. The Chieftains of the sunken house, after their fall from grace continued to live in Arnor, however the peoples of the Dúnedain were small and scattered and never rose again to the power of old, before the time of Aragorn Elessar.
Onto Aragorn's claim. Aragorn himself never claimed the Kingship of Gondor, he himself unfurled the standard of Elendil and rode forth into the Battle of the Plennor bearing it, however he would remain outside of the gates, furling his banner and naming Imrahil temporary Lord of the City. It was in disguise that he entered the city and the Houses of Healing, and healed Merry, Éowyn and Farmir, in accordance with the prophecy: “The hands of the king are the hands of a healer, and so shall the rightful king be known”. Aragorn then left the city, hooded and cloaked, and yet the people of Minas Tirith followed him, for they had heard rumours. However, the next morning they only saw the banner of Dol Amroth and wondered if the Return of the King had been but a dream.
It was only after returning from the Battle of the Morannon and the destruction of the Ring and Sauron that Aragorn was crowned outside the gates of the city, and the people had all accepted him, he had not set forth to claim the city from them.
Then Faramir stood up and spoke in a clear voice: ’Men of Gondor hear now the Steward of this Realm! Behold! one has come to claim the kingship again at last. Here is Aragorn son of Arathorn, chieftain of the Dúnedain of Arnor, Captain of the Host of the West, bearer of the Star of the North, wielder of the Sword Reforged, victorious in battle, whose hands bring healing, the Elfstone, Elessar of the line of Valandil, Isildur’s son, Elendil’s son of Númenor. Shall he be king and enter into the City and dwell there?’
And all the host and all the people cried "yea" with one voice.
Return of the King: Book 6, Chapter V, The Steward and the King