PeerBox was designed to offer the highest level of privacy possible by cutting out every middleman. That does come with a little less flexibility than regular email, but you have several options. You can install it on a Raspberry Pi or any small machine that stays on, which gives you near-permanent availability. You can also simply agree on a time window with your contacts for message exchange. And actually, we're considering releasing a VPS-compatible version soon, which would do exactly what you're describing. Stay tuned!