If you ream it, that's going to mean some part of the headtube where the races fit will be thinner than they're designed to be. That'll be a weak point.
Given that it's a steel frame, perhaps setting it back to circular (or a lot nearer) using a vice might do the trick. A friend has a newish Specialized and was running very loose headset for ages (I moaned at him continually), but when I replaced his headset, there was no ovaling at all, even though he pounded the bike. So I'm guessing that perhaps it's a softer metal than other headsets and therefore might bend back more willingly and with less structural impact. Kinda dodgy on such a critical part of the bike, but I'd prefer that to reaming.
If you ream it, that's going to mean some part of the headtube where the races fit will be thinner than they're designed to be. That'll be a weak point.
Given that it's a steel frame, perhaps setting it back to circular (or a lot nearer) using a vice might do the trick. A friend has a newish Specialized and was running very loose headset for ages (I moaned at him continually), but when I replaced his headset, there was no ovaling at all, even though he pounded the bike. So I'm guessing that perhaps it's a softer metal than other headsets and therefore might bend back more willingly and with less structural impact. Kinda dodgy on such a critical part of the bike, but I'd prefer that to reaming.
Good lesson for the rest of us re headsets.