Hi Reman, nice to hear from you. I have a '48 copy of Booker, which has an illustration of the 350 WD/CO engine on page 19. Your engine should look broadly similar, ie: oil filter under timing case, and vertical finning above the exhaust. [The later Clipper/Model S head had horizontal finning only.] Your forks should have the cast top yoke with integral speedo, like the Model G; rather than the larger 'casquette' fitted to the Clipper and post '54 Bullets etc. [although I think I did see an advert for an 'S' with the casquette, but that may not be original?]
From your description, and the pictures in Gordon May's excellent book, [worth getting] the advertised '36' Model S may actually be a '37; [the '36 engine seems to have had a forward sloping cylinder.], but exact year dating is notoriously unreliable, so who cares!
Now you know yours is 'real' have you arrived at a plan for it yet? I haven't got a Model S, but I have two mid '50s Clippers, and two J2 500 rigids, under rebuild at the moment; so I've probably hit most of the likely major problems you will encounter. If of any use you can e-mail me on stvwheeler@aol.com so I can send pictures etc.
Cheers, Steve.