I have no idea personally but thank you for bringing attention to it. I *LOVE* that BSA A50 racer you linked to, was not aware of it before and very cool. (I have some unit A65s and singles so a cool bike like that is great to see)
Not to hijack your thread but I found it super interesting that A50 ran a Magneto off the back of the timing case. Did not think that was possible. (Would love to see some internal engine details on that)
I would THINK you should be contacting the BSAOC and see if there is records of your engine, Be very interesting to see what turns up.
Have you read the material from Val Pages autobiography? It appears he was not a big fan of the twins. (Goldstar man) but he was tasked with engineering and process improvements on them which led to eventual great success. Perhaps your motor is a later test piece.