Can you flip Zhonya's Hourglass to save a unit after Volibear's ability has started dealing damage to multiple units?

Ruling: You must flip Zhonya's Hourglass before Volibear's ability resolves and deals damage. Once Zhonya's is face-up, if multiple units die at the same time from Volibear's damage, you choose which one to save.

Sequence:

• Volibear attacks and his trigger goes onto the chain, with damage divided among targets
• You must react with Zhonya's at this point (before the ability resolves)
• Zhonya's resolves and is now face-up
• Volibear's ability resolves and deals all damage simultaneously
• All units that would die from this damage die at the same time
• Zhonya's triggers and you choose which unit to save

Nuances:

• You cannot use a Reaction in the middle of something currently resolving
• If you allow the ability to deal damage and kill units without flipping Zhonya's first, you cannot then use it to save one
• Actions and non-reaction speed abilities cannot be used in response to on-attack triggers