I don't at all like the idea of being logged, especially since you need to log not only /say, but also all other channels, including the seemingly private /tell channels, as you can easily abuse someone via /tell if they don't know how to work the /ignore feature (even though one should never ever trust anything that one doesn't want to be broadcast in the news to any unencrypted internet link, there are things that just don't justify the effort but on which privacy must still not be broken without good reason, like /tell and /group).
However, given the obvious necessety (and the fact that I've experienced similar situations before) a backlog of 5 minutes seems tolerable to me. I've wished for a /backlog feature these times, so if it's implemented in the suggested way (severely time restricted unless /reported) it's fine with me.
There isn't that much of an issue of /report timing out after 5 minutes. If you think it's required, one can just keep entering /report every couple of minutes to keep it running, no? And while I don't generally believe in second chances, the suggestion about the system warning the one being logged about that fact does make sense, especially since it gives the system even more power in case the one still doesn't stop.