To joejack951: sorry for confusion, the mallet that I have used was indeed a plastic one called 'no marring mallet', used in woodworking for some furniture assemby; I think it is just common to call the thing 'rubber mallet'.
As for getting sealed bottom bearing in... thank you - interesting idea (I did not know I can do that on threaded setup) ... for the far future

Right now, I have not ridden that bicycle even once (I got it in a shape that is in my opinion unrideable). I am not 100% sure if it is actually going to work out for me. That is one of the reasons why I am leaving it's battered finish on it for now, just doing some de-rusting and touch-up-ing to preserve it. I actually thought about using $12 headset on it for now, but then changed my mind and went for a 'ridiculously expensive' one at $40
As for directions, they were VERY clear to put the headset cage up, balls down. They pictured them that way, and than they spelled it out in the text 2 times, first time simply as a part of installation instructions, second time really making the point of it. As I read them, when I saw the picture - I thought - they are wrong and still smiled, when I saw text in installation instructions - I thought - they are wrong but my smile faded, and when 2 paragraphs down they made special point of the bearing orientation in the upper case, I thought - what the #$%@ is going on, did I install them backwards?
After all, what is the point of the instructions if they provide wrong recommendation on the only step in the process that is easy to screw up?
All in all, headset works well. Smooooooth, and there is absolutely no binding nowhere, perfect rotation 360 degrees around, with just slightest friction that is likely result of well-packed grease.
I have overhauled headset on another vintage Fuji recently (factory one, have not seen much use at all), and that one was quite smooth as well, but when rotated about 90 degrees from straight, it would bind slightly in one area of rotation - I guess on that one some of the cups/races were not placed perpendicular to the steerer, either not seated properly or frame/fork not faced properly.