Tom, given its serial number (33517), your gun was completed in 1891, according to the appendix referenced at the back of Graham Greener's The Greener Story. With respect to the time consumed from start to eventual completion, this depended on the gun's grade: Higher grades required more attention and time. For example, my self-acting ejector G60 grade 'Royal' needed some 7-months before it was completed the following year. The building of lesser grades by Greener took much less time and was performed in a different area of the Greener factory. Only the best, specially selected craftsmen (10-12 men) built Greener's higher grade guns in a wholly separate area of the factory.
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Without informing photographs of your gun, however, I am at a loss to correctly identify it. Although, I would venture to guess that it is a Facile Princeps self-acting ejector or perhaps a 'Unique' action-ed gun, based solely on the fact that these candidates were in production at time your gun was completed. The 'Triple Wedge Fast' action refers to Greener's strengthening employment of Purdey-patented double underlugs/bites and the Greener carefully fitted cross-bolt in combination with a precisely bored barrel extension. The 'sterling steel' likely refers to a type of or marketing name for its damascus barrels. Greener's damascus barrels, by the way, if in good condition and possessed of sufficient wall thicknesses, especially those used on the company's higher grade guns, are perfectly serviceable to-day if one uses low-pressure cartridges of correct length. Greener used a high percentage (70%, as I recall) of steel in his damascus barrels. The lack of a safety is a puzzler, which might, as you conjecture, indicate an intended purpose as a pigeon gun or possibly, I would add, as a fowler.
Hopefully, Graham Greener can provide you a model number as well as a customer name. At all events, as has been previously suggested, you might want to post clear photographs of your gun here, in order to benefit from the combined knowledge and opinion of this site's well-versed correspondents. Regards, Edwardian.
W W Greener was a member of the second-generation family which had been involved with gunmaking from 1829 to the present day. Today the company still makes the finest sporting shotguns and rifles in its Midlands workshops.William Greener was the first to make guns.