You could have a feature that users could turn on in their profile to display if they are online or when they were last online, and have a setting to restrict it to certain times, so that other users can know if this person would respond to a post/needs response to a post. And then a "follow" feature, that just displays the timestamps for users that you "follow" in particular (because I imagine that if you follow someone you might not care about the age of their posts). Lastly, you can just have it as an option for any post "include timestamps," so that a user can let others know the temporal context of one (or all) of their posts. I think these 3 features together would solve all of the issues with timestamps while still retaining the engagement strategy you are looking for.