For whatever reason, your suggestion triggered a series of thoughts and experiments that led me to, I believe, a solution!
For the anomaly, you use the OnEvent "OnArriveAtAnomaly" to PerformAction "StoreEventChoice" and a separate "OnArriveAtAnomaly" to PerformAction "TriggerGlobalEvent"
On the event, you set CheckPlayerPrerequBeforeFiring to true and set the Prerequ to the stored EventChoice; then, under each event choice, use OnEvent "OnEventChoice" to PerformAction "RemoveEventChoice" using the stored event choice string.
I'm pretty excited and am going to play with this to try to have the event take over the existing window, if possible. But otherwise, this seems to work!
Thanks for the suggestion that, apparently, led to the right thought process! (and all the other suggestions and input along the way)