I'm not sure I entirely follow your argument. I agree that you can use some sort of heartbeat protocol or negative acknowledgments to determine whether writes occurred within a given time window (e.g., I haven't heard from the cluster, so maybe I missed an update in the time since the last heartbeat). However, in general, I don't believe it's possible to guarantee non-trivial convergence for fixed T and unlimited partition durations.

For any given T, if I partition each of your nodes for T+1 seconds, you won't be able to guarantee convergence--your nodes won't communicate. Am I missing something?