If he does not know the route itself how can he know that? Orcs can climb mountains too, they are born mountaineers after all. As an experienced orc-fighter Beren has to know that much.
? He is a native there. He has grown up with horror stories about the mountains. He knows his own land.
That explicitly stated there in the text. He was the only one to ever attempt such a feat.
The occupation has too little time to tighten to such a degree in the short amount of time. You have to remember that you have changed the story by removing several years from it so that Beren decides to leave just after having accomplished succesfully his revenge at the very other end of Dorthonion and having traveled back undisturbed to a location that was already known to the enemy without any trouble.
? If he has less than perfect awareness of the danger of the situation around him that makes him less prone to enter Ered Gorgoroth than more?
I've actually re-checked the Silmarillion. It does say little about his choice. Beren sees Doriath from afar while already in Ered Gorgoroth and decides to go there because he likes the look of the forest. It is not even clear he understands it is Doriath at this very moment - the description is a little vague - not necessarily restricted to his own perspective.
Here some citations (without page number, as from an online source)
https://archive.org/stream/TheSilmarillionIllustratedJ.R.R.TolkienTedNasmith/The Silmarillion (Illustrated) - J. R. R. Tolkien; Ted Nasmith;_djvu.txt :
About
Ered Gorgoroth in the
Silmarillion from stories
predating Beren:
Soon afterwards Ungoliant fled from the north and came into the realm of King
Thingol, and a terror of darkness was about her; but by the power of Melian she
was stayed, and entered not into Neldoreth, but abode long time under the
shadow of the precipices in which Dorthonion fell southward. And they became
known as Ered Gorgoroth, the Mountains of Terror, and none dared go thither, or
pass nigh them; there life and light were strangled, and there all waters were
poisoned.
(...)
Between Mindeb and the upper waters of
Esgalduin lay the no-land of Nan Dungortheb; and that region was filled with
fear, for upon its one side the power of Melian fenced the north march of
Doriath, but upon the other side the sheer precipices of Ered Gorgoroth,
Mountains of Terror, fell down from high Dorthonion. Thither, as was earlier
told, Ungoliant had fled from the whips of the Balrogs, and there she dwelt a
while, filling the ravines with her deadly gloom, and there still, when she had
passed away, her foul offspring lurked and wove their evil nets; and the thin
waters that spilled from Ered Gorgoroth were defiled, and perilous to drink, for
the hearts of those that tasted them were filled with shadows of madness and
despair. All living things else shunned that land, and the Noldor would pass
through Nan Dungortheb only at great need, by paths near to the borders of
Doriath and furthest from the haunted hills.
And here is the very passage
about Beren deeds after finishing his revenge:
Thereafter for four years more Beren wandered still upon Dorthonion, a
solitary outlaw; but he became the friend of birds and beasts, and they aided him,
and did not betray him, and from that time forth he ate no flesh nor slew any
living thing that was not in the service of Morgoth. He did not fear death, but
only captivity, and being bold and desperate he escaped both death and bonds;
and the deeds of lonely daring that he achieved were noised abroad throughout
Beleriand, and the tale of them came even into Doriath. At length Morgoth set a
price upon his head no less than the price upon the head of Fingon, High King of
the Noldor; but the Orcs fled rather at the rumour of his approach than sought
him out. Therefore an army was sent against him under the command of Sauron;
and Sauron brought were-wolves, fell beasts inhabited by dreadful spirits that he
had imprisoned in their bodies.
All that land was now become filled with evil, and all clean things were
departing from it; and Beren was pressed so hard that at last he was forced to
flee from Dorthonion. In time of winter and snow he forsook the land and grave
of his father, and climbing into the high regions of Gorgoroth, the Mountains of
Terror, he descried afar the land of Doriath. There it was put into his heart that he
would go down into the Hidden Kingdom, where no mortal foot had yet trodden.
Terrible was his southward journey. Sheer were the precipices of Ered
Gorgoroth, and beneath their feet were shadows that were laid before the rising
of the Moon. Beyond lay the wilderness of Dungortheb, where the sorcery of
Sauron and the power of Melian came together, and horror and madness walked.
There spiders of the fell race of Ungoliant abode, spinning their unseen webs in
which all living things were snared; and monsters wandered there that were born
in the long dark before the Sun, hunting silently with many eyes. No food for
Elves or Men was there in that haunted land, but death only. That journey is not
accounted least among the great deeds of Beren, but he spoke of it to no one
after, lest the horror return into his mind; and none know how he found a way,
and so came by paths that no Man nor Elf else ever dared to tread to the borders
of Doriath. And he passed through the mazes that Melian wove about the
kingdom of Thingol, even as she had foretold; for a great doom lay upon him.
It is told in the Lay of Leithian that Beren came stumbling into Doriath grey
and bowed as with many years of woe, so great had been the torment of the road.
[Citations' end.]
This is just an overview. This is not a story.
But even here it is said that he was driven out of Dorhonion by:
"an army was sent against him under the command of Sauron;
and Sauron brought were-wolves, fell beasts [...]
was pressed so hard that at last he was forced to
flee from Dorthonion."
You have already changed what little of a story there is by:
-removing Beren's Beleriand-wide fame as an orc killer (I do admit to reset that change a little)
-removing Morgoth's price on Beren's head
-removing Sauron personally chasing after him with an army of werewolves and monsters
-removing the four years of encroaching corruption that made all clean things leave Dorthonion
-making Beren decide to leave straight after his revenge and on his own accord by making a rational decission
This story has already been changed beyond recognition to have completly different dynamic.
Please do make it coherent, because at the moment it simply is not. - If you have changed it this far so that actually little is left of the original then please do change it farther - enough so that it does make sense again.
P.S.
Beren is a warrior who knows his land, not a foreigner who does not know what he is doing. He knows what Ered Gorgoroth is. He has grown up right next to it.
Going there was "
not accounted least among the great deeds of Beren" - it was a deed of a hero, he knew what he was up to when he entered there. But what has brought him thus far? In this version of the story there is simply yet no reason for it.
So some valid reason needs to be created.
And the time to set it up is EP2.
"Make the story make sense again!"