I rang the CAA with the question about obtaining an SEP class rating under my circumstances, and they actually do not know the answer! I've never held a PPL(A), and so even though my EASA licence now automatically lists that I have a PPL(A) due to holding an ATPL(A), it does not automatically mean that I hold an expired SEP. Indeed, they checked and confirmed that I have never held one. As a result, my reading of CAP 804 is correct and the requirements for me to obtain an SEP class rating are not covered by the document. They were therefore unable to advise me!
I was instead guided towards emailing a specialist department, which I have done but it seems I could be waiting anything up to 30 days for an answer. Something tells me it will be longer...
I'll ring Abbasair in the morning, and see what they have to say on the subject.