You can get the head tube reamed.
got an adjustable reamer at work. Not tried to ream a head tube with it
Ive just cut a head tube down so I could fit suspension forks to my BSA 20.
Just cut the tube to 4.250 inch. Then filed it to smooth, straight. Filed down inside.
To get the burred metal out.
Then looked at my box of cheap secondhand headsets. Picked out 2 cups.
Pressed them in...by closing the vice onto the head tube.
Fitted easily. No sign of bulging of the metal.
But I think the headtubes on these bikes are thinner at the top.
To get that stupid plastic bush in.
Mine wasnt tight on the frame.
Turned with the forks even after greasing.
Junked it