Fitting the proper headset on a Tokyo Fixed S2 frame

I am having a bit of a problem with fitting a good headset to a Tokyo Fixed S2 frame.
I got it off ebay, some 2 months ago, and I got a mint Dura Ace 7410 headset to fit.

The problem is that the D-A has a stack height of about 37-38 mm and it is too high for how long the steerer has been already cut. So I will consider a Tange Levin headset, in steel.

The real problem: is that, the headtube is not properly faced. HOWEVER the previous owned said that he also used a Tange and everything sat fine. (I doubt this, as there is a difference of 1 to 2 mm between faces.)

The funny part: I live in Romania, and no one has a facing tool here. I repeat, no one.

The question: is it possible that the Tange is more "flexible" so to speak, and would not require facing? Would I be able to get away with one without concerns of play, breaking, cracking etc?

Help is much appreciated...

Please? Anyone?

if you have a selection of metal files and a carpenters square:

you could have a go at it, but very carefully or you'll write the headtube off

you'll have to establish a datum line at each end so that you know which parts of the edges of the cylinder to file down yet still keep the whole headtube square

tange levin in steel are good headsets with a low stack height so at least that part is in your favour

Can't believe there aren't facing tools available there.. And, I'm sorry my friend, but facing is the most important part of proper headset installation.. The race/bearings/cups will wear unevenly when not flush, so that'll fuck up the headset..
Btw, if you do get access to a facing tool, you might be able to shave off a bit more off of the headtube, allowing for a higher stack height headset to be used i.e. that DA one..

Yes, I know how facing is important :( However I am still looking for a solution before filing the head tube. This weekend I am going to a flea market where they have cutter heads from ex-communist machine shops. Maybe I can build a facing tool. I think I could use a threaded rod and an alloy cone for the other end.

However, about the Dura Ace headset, I did a mockup install and I only have room for the first nut, the steel washer and the top nut do not fit right now. At least 3 mm are missing, considering I can get away with only fitting the top nut, without spacer/washer. This is a real shame, as that D-A headset is a beauty.

If you really want to use the DA headset fit the first nut ie the top cap and loctite it in place. The locknut was invented before anyone had invented loctite. But whatever, face the headtube first, your new DA headset won't last anytime at all if you don't.

This is late, but I thought I'd post...I have sent the frame to the capital city, Bucharest, to a shop where they are Park Tool dealers and have the facing thing. It came out great, and now the Dura Ace headset fits perfect. There is no steel washer, but it does not bother me. Might Loctite the top nut after a couple hundred miles, though.
Thanks everyone for their advice.