I've more than one stayer bike, mine are from late 30s to early 80s. I've spoken to former pro stayer riders, coaches and mechanics so I'm aware of all the good points you have addressed.I'd take a look at as many period photos of stayers as you can find.
In my experience they are very varied and just modified regular track and/or road bikes with reversed forks and smaller front wheels and relatively upright stems, compared to the steeper geometry of track stems. Although, that being said a very few manufacturers did offer specific models.
Remember that stayers sat far more upright in order to keep their lungs more open for as high an air intake as possible.
In my opinion those extra long stems were frequently homemade, or made on site at the velodromes workshop, so remodelling your example above is not out of the question.
That said I also know that those kind of stems - particularly the one shows in my pic - were frequently custom made by mechanics even if they can also be found in some pre WWII catalogs and they were available in various lenght or cutted to measure.
I'm not really into repro stuff.