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Nosotro Tehuti, damn fine posting there!
Ereshkigal is indeed not Tiamat, for all ther reasons you stated.
For the newer people, please understand that I am not a magickian using the Necronomicon, I'm a prietess of Ereshkigal. I post here, because it's the best place to post about Sumerian deities, so I may not be very aware of what the Nec says about something versus more traditional mythology.
However, what I have read from the Nec, there does seem to be some back and forth about Ereshkigal being an Elder God, versus an Ancient one. She is not Tiamat, She is not an Ancient One, She is one of the Elder Gods, performing her role in the universe that exists now. She's not all warm and fuzzy, but neither is She evil.
Many of the Elder God may be seen as evil, or mistaken as Ancient Ones. People don't seem able to grasp the fact that Gods are different from us very well. They think different, they act different and are different in essence from us. Especially in our current society that values political correctness and the fallacy that everything is true, deities/entities like Ereshkigal, Nergal, Pazuzu, Humwawa, Lilit, et al will typically be seen as the embodiment of evil. Yet, they are not, they just don't fit into the "shiny, happy people" worldview that most want to delude themselves into believing. Death, disease, war, etc all serve purposes, and their ends must be accomplished. Those deities that rule over such are simply "doing their jobs".