really a pretty cool bike, all things considered. And I'd be willing to believe that it is a Fuji...we might be able to get a better-documented answer if you provide a serial number. There are people here who have compiled some Japanese serial number statistics.
Back to the headset. The underlying problem is that the fork isn't original. The fork was hacked into the frame, cleverly, by using parts of two headsets...thus mitigating the need to hacksaw off the extra fork length of the replacement fork. Essentially, pieces of a second headset were used to space out the extra long steerer. All conjecture on my part, but I'm right, of course.
I think that you should look under the top tube and under the down tube, where they meet the head tube for signs of buckling...may not be an issue, may be. The fork was replaced for a reason...
And, while we are on the subject of the fork, what purpose does that bolt between the fork crown plates serve?