Ovalised Headtube - solutions?

I have a frame that I'd like to get back on the road, but I'm having trouble fitting the headset.
The problem is that the head tube no longer seems to be round. It's only out by a fraction of a mm, but it's enough to make fitting the h/s impossible for the meantime.... is there anything to be done about this? Some way of making it round again?
The bottom of the headset went on OK.

Is it a new headset? Maybe just needs the headtube facing?

getting the headtube reamed may help but it might be totally fuct

has frame been crashed ?

No not crashed, just ridden for a while with a loose headset.

• The headset's fine, just took it from another bike.
  
  

Think reaming might be overkill, I imagined some of of homemade tool that would basically just be a big piece of slightly tapered steel that ended up exactly the right diameter... and which could then be removed with a h/s rocket or somesuch. Does this sound stupid?

I have a fairly bad track record with this kind of thing.

steel frame, btw.

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.