Mythology is constantly re-interpreted, even within the culture in which it is told. The only reason why we modern people think of stuff as "original versions" is that that is the version that got written down - I'm pretty sure Ancient Egyptians and Sumerians had multiple myths telling the stories of Set and Inanna, all of them different depending on who was telling them, where they were from, and when they were being told.
Respecting the source-material has less to do with being 100% accurate to the written-down versions, and more to do with staying true to the spirit of the material - and most of all, do your research. You say you want to use Ishtar instead of Inanna for your story, but that you "didn't see" an ending to the Ishtar-story - research more. Read more. Find out how that story ends, if an ending exists, and then decide what to do with it.
As a Swede, I'm long since used to people getting the Norse myths terribly, terribly wrong - and it's usually mistakes they could have fixed if they, you know, just read some actual books instead of skimming Wikipedia. Their mistakes don't offend me - I'm an atheist living in modern Sweden, I'm not going to be offended by misrepresented Norse myth - but it does make me roll my eyes, because it would have been so easy to get right - and in a lot of cases, a lot more interesting.
I mean, I see tons of stories about Loki and his betrayals of his fellow gods/giants - but very few stories about the giant wolves Skoll and Hate who devour the children who move the sun and the moon across the sky; or about that one time Odin and his real blood brothers killed the frost giant Ymir and fashioned the entire world out of his flesh (did you know the clouds are actually Ymir's brain?).
Dig deep into your source-material, and you might find it's a lot more potential there than you thought.