It might be better if you have one group of Demigods against another with a differemt agenda for the end. Such as one wants the demigods to have supremacy and the other just wishes for a full restoration of the world before the event. As for this idea, whose character would win? I'm sure posters would be pissed if they spend a lot of time and effort into this only to find that you're steering the contest into your favor. So ultimately even if your character legitamately won, it might still irk someone.

As for how they'll end up at the same location, maybe it could be almost like a shared dream? Each of the characters who are affected by the event would enter a sort of shared conscioussness where they are being told the rules of the battles to come by the current God, explaining that whoever won would be the successor to the Power. The actual ruins could an arena and the event lays a kind of compulsion over those involved to go.