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Well, technically Greater Invis lets you do any action with a chance (Based on Stealth skill) to remain invisible.

It however, doesn't fix the problem of the nearby Druids having Truesight and being able to see through invisibility (It being "Greater" does not make you any more invisible, you're vulnerable to Truesight like any other form of concealment)

Had the Druids not randomly been one of the only entities in the entire game to be given permanent Truesight, then Greater Invisibility (As well as Darkness/Fog) would allow you to pick up the Idol without being detected.

Yes, and that is very sad. Although there are many ways to avoid combat. If the game offers freedom of choice, then for some reason, when it comes to combat, freedom of choice is taken away.