Hi Marcus,
With its build date of early 1911, it's probably a bit of a corporate transition gun. As you may know, old Ted (E.J. Churchill) passed away 16 November 1910, and the running company was then taken over by his nephew Robert Churchill. During this time, (according to the 1906 and 1914 price lists) they went from simply listing their better guns as "best-quality hammerless sidelock ejector" at 70 and "best-quality Anson & Deeley ejector" at 60, to the range of model names that we are familiar with now, in particular the "Hercules finest-quality Anson & Deeley ejector" at 50guineas.
If it has the EJC monogram, and the rest of what you describe, I would think that it would have been bought, and built as one of the previously described "best -quality" A&D ejectors.
Just FYI, the description in the catalog I have (circa mid to late teens) reads;
" The 'Hercules' model, finest quality. This gun is made on the Anson & Deeley" principle (without side locks), of modest appearance, built for strength and solidity. All other particulars as the "premier" model.
Price per gun ... ... 50 guineas. "
If you can post some pictures, it would be of great help.