I have been watching your postings with interest. John Underhill is the club registrar and he will be able to identify your bike for you properly (unfortunately he is not contactable over the net).
However, I now own the 2 Speed Sports Squirrel which is in the picture you linked in one of your messages. It is nearing (!!) completion of a rebuild. My bike’s frame number is 2856 and te engine number Y2178A both of which have been confirmed as 1929 items (although not necessarily a matching combination).
I think (and someone will correct me if I am wrong) that all of the Scott works records except those for 1928/9 are with the Vintage Motor Cycle Club’s libraray in Burton on Trent. Members are able to attend and view them and also might receive (without a personal visit) a validataion certificate with a lot more information – such as dispatch date, type of magneto and carb. and dealer’s details. You might like to approach them.
I think that your bike is earlier than mine. The Y pre-fix applied to standard and Super Squirrel 596 engines (the 1929 sports squirrels were all Supers – I think). The number you have is a 1926 sequence engine so best guess is that it is a standard 1926 596 engine.
Frames are more difficult to date as they did not leave the factory in sequence. However I am aware that 773 is a 1925 frame . Yours might well be 1926.
The Sports Squirrel was a late addition to the 1929 catalogue (it did not appear in the catalogue at all in Autumn 1928). It’s only real difference from a 2 Speed Super Squirrel was the “Sports ” tank which I think was available separately before 1928 in any event. Yours might have an early sports tank or a later addition.
Finally, Al Perry in New York has a 1930 2 Speed Sports and might be listening in. He helped me with measurements for repairs to my tank – but I know that he is the other end of your Country!
Finally, finally see my postings earlier regarding 20″ tyres. Avon still make the ribbed (raher than blocked) tyres you seem to need for racing. They should be readily available in the States – otherwise let me know and I can source some here for you.
Happy Scotting !