Yeah, exceptions are not enough for fully reconstructing the problem! I'm not sure this can and should be necessarily fixed by changing exceptions, though. It is often the case that you need a deep trace to understand the problem and mainstream tooling is not prepared for that (I wish rr to be more widespread).
For algebraic effects: I too had keen eyes to Koka and think that it might be the future. What I don't know is how to make effect types mostly invisible to users without sacrificing its power. I had been experimenting with dynamic scoping in my mind, but that feels unsatisfactory.