I'm not proposing a low-latency interactive approach, so latency triangulation shouldn't apply. In my example mechanism, we always have to wait a full day until sending any reply, so there's no event that an attacker can use to measure latency from.

Edit: the beginning of this research is the Dining Cryptographers.

https://en.wikipedia.org/wiki/Dining_cryptographers_problem

Although Chaum's solution has terrible availability properties, it's unconditionally secure against outsiders!