I ran into a similar problem with my Austrian Steyr, only it was the bearings that simply got rough, so I was able to carefully rebuild and adjust it with a much larger # of loose ball bearings so as to finally restore accurate steering.

I concluded that the only practical solution to obtaining a replacement headset would be to buy another low-bid Steyr Clubman bike off of Craigslist, and sure enough another couple of them have come along for under $50. I didn't end up needing a replacement however, it was sufficient to discard the 14-ball retainers and replace with 26(?) loose balls together with rotating the cups and crown race.

For the OP's threading dilemma, I have many times saved similarly cross-threaded bb cup threads by removing the crooked cup then screwing it back in, using many taps of a hammer to level the cup as the cup is slowly started into the bb shell.

I'm sure that there is a good chance that this same method can be used to get the threaded headset race started on the steerer straight!
All the parts are steel here, and this bodes very well for restoring a proper fit in my experience.
Patience wins the day and I wish the OP best of luck in getting this bike back together.

A good (and frequent) eyeballing during initial installation should do the trick, and there is usually more than enough metal in the right places to get a solid connection.
The cross-threading and subsequent re-threading doesn't so much remove metal as it just moves it around. It's not like having a tap going through crooked, which would cut the metal away.