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I had this issue with my Koga Miyata. I tried to look around for a quick fix but most advise is don't mix and match the parts and it is not worth damaging frame or bearings. In the end I spent the extra on a JIS Dura Ace headset. it's not worth messing about for the sake of a few quid IMO in the end I was glad I did anyway as ended up with a much better functioning and looking part.
Mine is a 1979 steel frame. Not sure about getting it reamed I was given the advice that it would be better to get the correct size.
If you use the search function on here you might find a previous post with some info.
good luck with build!