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So, still no joy? The gas cap is still stuck?
Here's an old thread on the Vintage BMW forum with someone who had the same problem. Doesn't appear that there was any solution. I posted about my aftermarket cap with "HK on the top. The locking mechanism uses the key that I initially posted.
https://vintagebmw.org/forum/viewtopic.php?p=79189#p79189
I found some older catalogs, one from Butler & Smith and one from Flanders. The B&S image doesn't look anything like what you show, while the Flanders offering does. In both cases the key shown is more of a standard key shape. However, your image almost looks like it would take the "nail" ignition key right down the center.
https://bmwdean.com/butlerandsmith.htm
https://www.w6rec.com/duane/bmw/flanders/page14.jpg