The frame number is a mystery but that is no surprise. Excelsior did strange things with frame numbers around about this time. I have a couple of circa 1930 Excelsior frames with no number at all.
Essentially I think this is a circa 1931 Model A11 Excelsior. This was their 350 OHV two port Sports model fitted with a JAP engine, Burman 3 speed handchange gearbox,twin downtube frame, etc, etc. Everything is exactly as in Mateusz' photo. The final confirmation is the odd saddle. If you look carefully it seems to be similar to a BSA of the time with a central mounting post yet is also spring mounted at the rear.
As fitted by the factory the central post is actually an upside down L shaped casting/forging with a forward facing arm so the saddle pivots at the front. As far as I know its unique to Excelsior. I don't know of any other make with such an arrangement. If the original saddle failed owners could replace it with a central mount saddle so you find some strange arrangements. Mine have a mixture of original factory system, replacement central mount saddle and a horrible home made replacement bent pipe arrangement so the original factory part must have been a weak point.
There are photos of the A11 Excelsior to be found in the Excelsior Gallery of
www.cybermotorcycle.com . That owner claims it be a 1930 model but it can't be as Excelsior didn't catalogue a 350 OHV model in 1930.
Cheers,