Take the new headset and thread it on as far as it will go without using great force. Now, support the steering stem as close to the threaded nut as you can and give the nut several taps, all the way around, with a hammer, ensuring to not damage the appearance of the head nut.

Now, after tapping the nut a few times, attempt to thread it on again. Likely, it will thread easier and go on a bit further. If so, repeat the procedure until the nut fits with little or no binding.

This is an old millwright's trick to get a nut to fit without going all the way to the stores counter to get a proper die or chaser or whatever.

Give it a try, you have nothing to loose.