Reference your first paragraph Fred............crossed wires, I think

I don't doubt for a moment that Sowerby patterns 1224 and 1231 carry diamond lozenges which will date them to 31st May 1877 - also that these lozenges are found on Cottle;s 'angular' shaped pieces.
I was simply drawing attention to the fact that there is an obvious case of confusion somewhere along the line insofar as........... Simon Cottle links these Sowerby patterns 1224 and 1231 to the Kew Board of Trade Registrations Nos. 310595 and 310596 - this is wrong, and the objects are completely unrelated.
His linking of these is misleading to anyone who is involved in cross-checking Registration Nos. with factory pattern data. Much time is wasted due to the fact that the Rd. images at Kew do not match images of the Factory Patterns - despite carrying the same No. in Simon Cottle's book.
The bottom line is simply that these two Board of Trade Registration Nos. were not allocated to these two particular factory shapes/patterns.
My earlier suggestion was that, possibly, Simon Cottle had not seen the Kew images and had simply worked from Sowerby archive material - in which case perhaps we should blame Sowerby for sending the wrong images to the Board of Trade at the time of Registration.

Unlike yourself, I don't spend that much time involved with C19 pressed glass - neither am I that familiar with other data in Simon Cottle's book, so have no idea if this mis-linking is a one off, or if there might be other instances.
From my experience of taking snaps at Kew, it's apparent that Sowerby's Registrations with the Board of Trade during the latter part of the C19 were prolific to say the least - and so very obvious from looking at the size of the factory's catalogues, I just wish they hadn't used that purple ink that tends to fade with time

P.S. wish you every success with your project of 'gallery of reference photographs of Sowerby glass items'