I feel like the Secret Chamber/Moat interaction is a good model.
Here's the precedent: Let's say you have SC + 4 other cards in hand and a Moat on top of your deck. When an attack is played, you reveal SC and find the Moat, and return 2 cards to deck, keeping SC and Moat in hand.
Now, IIRC, you can still reveal Moat to get its protection, then reveal SC again again to return Moat back to the top of your deck.
That's a clear case where you were not choosing to order SC before Moat -- you couldn't have, since Moat wasn't even in your hand when you began to resolve SC. Yet you're still allowed to reveal Moat, which suggests that new cards put in hand during the first reaction's resolving are fair game to be revealed.
Conceptually, this suggests to me that when it is your turn to respond to an event -- e.g., an attack being played or the trashing of one of your cards -- you in fact choose when the window to stop responding to that event closes. So the first play of the SC resolves, but you are not choosing to pass priority (as they'd say in MtG, I believe) to the next player, you're keeping priority, and the event that triggered SC's reaction is still hanging in the air to be reacted to by Moat. (Likewise your second SC play.)
In the MS/Cultist example, the fact that you discarded a Market Square seems immaterial to me, given the above.
All the other reactions are multiple reveal, right? So why not Market Square?