Thanks for the further comments.
One of the two extra 12-28 dies I said I’d ordered was described as a 13/16” TWT (Threadwise Tools) split die.
It arrived today. You can see from the photo that what I was sent is in fact another Völkel.
I tried it out on some EN1A turned down to 5.4 mm with only a small chamfer. The die was put in a 13/16” die stock and the split was opened (though only slightly) for the initial cut. The die didn’t even hesitate to start cutting and it completed the cut with very little effort.
I then turned another piece of EN1A down to 5.3mm with the same chamfer and tried the first die; even with strong spring pressure bearing against the back of the die stock, the die simply would not begin to cut, and we were in dog point territory again.
Out of curiosity I turned the die round in the die stock so that the unlettered side was the leading side. I tried again. The die started to cut and I completed the threading.
I turned down another piece of EN1A to 5.4 mm with a minimal chamfer and tried the original die with the lettered side leading. No way would it start cutting. I flipped the die to have the lettered side facing away and tried cutting again; even though it didn’t start cutting as quickly as the 13/16” die had, it did begin to bite fairly soon and I completed the threading.
It would appear that what Howard said a day or so ago about the main chamfer sometimes not being on the lettered side, as you might expect, may be the explanation here after all. I’ve photographed the original 20mm die from both sides and you can decide for yourselves which side looks like it has the primary chamfer; I confess I can’t tell for the life of me. The most perplexing detail is that whilst the chamfers look the same, one is almost impossible to start threading with even when the turned diameter of the stock is way below the basic major diameter.
On the subject of the through-the-teeth diameter, the 4.23mm shank of a 4.3 mm drill will pass through both dies in their resting state with a zero clearance fit. It is marginally tighter on the 13/16” die.
The first two images show the new 13/16” die.
The last two images show the 20mm die chamfer from both sides.



ETA: Jason, the silver steel was marked 5.5mm, not 7/32”.