I've finally found the IRC gateway to be good enough for my needs. However, it still isn't quite as good as screen+irssi+shell server, one final piece of the puzzle remains, and that is to stay persistently logged in.
Therefore, I'd like the following;
1. An option when you register with the transport to have "persistent logins"
2. When this option is enabled, the gateway will keep you logged in and keep a log of the last 24 hours in those channels if the user is offline. It also should be able to handle PMs. This is so that I can receive offline messages over IRC, among other things.
After this I can finally ditch Screen and the somewhat cumbersome PuTTy in favor of Psi. Would this be possible? :)