Your problem is going to be resource scarcity. Remember, the Med civilizations were already trading as far away as Britain to get the tin needed for their bronze. I suspect that they can't continue a WHOLE lot longer without switching to iron.
Bronze Age civilizations were already using iron, and Iron Age civilizations still used bronze. The British/Cornish tin industry prospered into and after the Iron Age. In fact the last mine was closed in 1998.
Bronze Age civilizations weren't less advanced than the first Iron Age ones. They just happened to be destroyed shortly before that technological transition. And perhaps the collapse and its destruction of trade was the catalyst that made iron more cost effective than bronze.
If the late Bronze Age empires persisted, they would eventually have expanded their use of iron, and abandoned chariots when other forms of cavalry became more effective on the battlefield. Just as later medieval empires adopted gunpowder when it was available.
Basically, how does human society develop with either an averted or muted Bronze Age collapse?
How does the balance of power in the Near East evolve as civilization spreads out from the fertile crescent?
How do Bronze Age powers adapt to nomadic migrations and what does the greater continuity of civilization do for the retaining of knowledge?
I don't know much of anything specific about the time period and asking these sorts of questions is usually a great way to jump into a topic.
Without the Bronze Age collapse, the Hittites and Egyptian empires survive. If the Phoenicians become influential at all, they are vassals to Egypt. Eventually, perhaps the Hittites and Egyptians cause their own mutual destruction as Rome and Persia did, but it would take some time. But as the centuries go by, they could perhaps settle their differences and destroy Assyria.
Aramaic may or may not still become the predominant language of Mesopotamia, it depends on the interactions between the three empires of the Near East.
