I agree that the next session wants conclusions, not the whole transcript. What I've seen working with people on this is that a summary only has what the summarizer prompt asked for, and what they need from an old session changes depending on what they're doing when they go back to it. With the full session still around, they can just ask it again.
Porting is also cheap, since it's just a format conversion. Getting a new session back up to speed from notes usually isn't.
Concurrent sessions is a separate problem, and I agree that a message is the right shape there. Where portability helps is that different harnesses are good at different things, so you can start a task in one and move it to another that's better at the next part, without starting over.