I don't know if there is an actual relic. I don't think there is really. I don't think many people would be familiar with its notion even as fable, legend or myth, but then again who had heard about the Chachapoyan fertility idol or its like? I think it could work even though many may not know about it.
Like you say RS, referencing it and using its theme I think could work well as an analogy or parallel to Indy's life or at least plenty of his activities.
I hadn't thought about an antagonist but there would have to be one of course. Whether another rival archaeologist, secret organisation or government agency the possibilities are wide open. It would be set in Syracuse, Italy in keeping with the myth.
But we do need an Indy who is in charge of what he is doing. We need that ambitious glint in his eyes again, because there should be plenty of walk left in his Aldens even at 70yo.
ps the nuclear age was referred to as the worlds' Damocles sword by Kennedy, so it might be quite apt as a theme.