I haven't been able to follow the entire discussion and I haven't read the related texts (Tony Smith's book, Cyril's articles, etc.), but I'd like to make one general remark.
If I understand correctly, Cyril rejects the idea of the 'application' of a logical method (not only Hegel's) to any theoretical purpose. It's not right to split the logical method from the particular object "it describes." This -- he says -- stems from the division of intellectual and 'manual' labor.
In my view, distinguishing between the rules of thought that describe an object and that object itself is an elementary operation (abstraction). Just by naming things differently -- as Cyril does -- this operation is performed. Mentally isolating those rules (as if they were 'tools' separate from the object of labor) and extrapolating them to dissect other objects seems like a necessary task for anyone trying to think the world. That such extrapolation may be unwarranted -- say, due to essential differences between objects -- is another thing altogether. I think that, in the context under discussion, the term 'application' is properly used.
I guess I'm making a remark that is parallel to one I made before, namely that Hegel's Logic and Marx's Capital are, yes, historical -- but also humanly relevant in general. It seems to me that in Cyril's mind such 'general human relevance' is trivial, but I don't see it that way.