Have you seen the AskHistorians book list at https://www.reddit.com/r/AskHistorians/wiki/books and under it? Are any of them useful for you? There are at least a few applicable ones in the Europe page, and rather more in the Middle East and North Africa page (though on that page, the year of publication isn't listed, so you have to click through to each book in turn).

I'm not a mod, so this is just an idea from another reader: if you get any good suggestions, maybe you'd feel like composing them appropriately for the book list and message the mods? Surely they're willing to consider new book suggestions even from non-flaired users, if there's good cause to think they're good books and there's little work in including it?

This is not to discourage discussion. More questions, data and debate are welcome.

The Oxford Handbook of the State in the Ancient Near East and Mediterranean is a good place to begin for all of the above societies.

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I provided some reading suggestions for the Minoans a couple of days ago in Good book about Minoan civilization?

For the Mycenaeans, I recommend beginning with The Mycenaeans by Louise Schofield and the Oxford Handbook and Cambridge Campanion referenced in my post above. The Mycenaean World by John Chadwick and The Mycenaeans by William Taylour are now badly out of date but still useful. Mycenae: Agamemnon's Capital by Elizabeth French is an excellent overview of Mycenae.

Documents in Mycenaean Greek (2nd edition) is a decent overview of Mycenaean texts with a good collection of translations. A long overdue 3rd edition is in preparation, but there's no telling when that will be published.

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For better or worse, most books on Iron Age Anatolia are specialized volumes and terribly expensive. I've tried to pick the most readable and affordable options, but many below are still fairly expensive.

In the Land of a Thousand Gods: A History of Asia Minor in the Ancient World by Christian Marek and Peter Frei is a good place to begin for a broad overview of Anatolian history.

Ancient Turkey by Antonio Sagona and Paul Zimansky covers Anatolian archaeology up to the Lydian period. Joukowsky's Early Turkey: An Introduction to the Archaeology of Anatolia from Prehistory through the Lydian Period is a couple of decades out of date but still very useful for a site-by-site analysis. The Oxford Handbook of Ancient Anatolia contains several chapters on Iron Age Anatolia.

Roosevelt's The Archaeology of Lydia from Gyges to Alexander discusses the Lydians from an archaeological perspective, and Lords of Asia Minor: An Introduction to the Lydians by Annick Payne and Jorit Wintjes takes a more philological approach. Neither is an especially riveting read, so I recommend beginning instead with The Lydians and their World edited by Nicholas Cahill; the essays, along with others, are available on the Sardis Expedition website.

Phrygians: In the Land of Midas, in the Shadow of Monuments is a superb introduction to Phrygia. The recently published exhibition catalogue The Golden Age of King Midas is also pretty good, though it focuses primarily on Gordion.

From Lukka to Lycia: The Land of Sarpedon and St. Nicholas is a good place to start for Lycia. Trevor Bryce's The Lycians in Literary and Epigraphic Sources is dated but still very helpful.

For the Neo-Hittite kingdoms, there's Melchert's edited volume The Luwians, now heavily out of date in places, and Trevor Bryce's The World of Neo-Hittite Kingdoms, which is also somewhat out of date.

Urartu: Transformation in the East is the only decent overview of the Urartians I've found, but it focuses on Urartian sites in Turkey at the expense of those in Armenia and Iran. It's in need of an update, but Urartian Art by Maurits Nanning van Loon is available for free online.

I also recommend the video lecture The Syro-Anatolian City States: A Neglected Iron Age Culture, courtesy of the Oriental Institute in Chicago, and the 5-part video series The World of Phrygian Gordion courtesy of the University of Pennsylvania.