Join Date: Oct 2004
Location: DC / Maryland suburbs
Bikes: Homebuilt tourer/commuter, modified-beyond-recognition 1990 Trek 1100, reasonably stock 2002-ish Gary Fisher Hoo Koo E Koo
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I think you must have it backwards, a 27.0mm (JIS) headset will be *too loose* to fit a frame/fork meant for 26.4mm (ISO) headsets. See Sheldon Brown's headset sizing: http://sheldonbrown.com/gloss_ha-i.html#headset
If you are trying to replace the 26.4mm (ISO) headset with a 27.0 mm (JIS) headset, the JIS will be TOO LOOSE. If that's is the case, then you should return the JIS headset and get a properly-fitting ISO headset. Since ISO is the modern standard size there's a better selection anyway.
If you're trying to replace a 27.0mm (JIS) headset with an 26.4mm (ISO) headset, then the ISO headset will be too small to fit, as you've described. The solution in this case is to machine the fork crown to a slightly smaller diameter to fit the ISO fork crown race. I think a pretty well-equipped shop will have the equipment to do this.
I guess you could mix-and-match the races from the old and new headsets. That might work okay, but then again why replace the headset if the races are good?