An important thing to emphasize is that the relations within the core do not imply that the theories regarding the data must be similar. For example, while Ricardo accepted Say's Law, Marx clearly rejected it. Hence, the core is compatible with alternative theories of output, and similarly about the determination of real wages and technological change. The core is flexible and capable of encompassing different theories.
Further, nothing precludes the existence of feedback mechanisms and relations between the data of the system in classical analysis. The level of surplus might certainly have a relation to output, and that is central for the theories of accumulation, but those relations lack the generality that is attributed to the core relations. In those, less rigid relations, the role of institutional and historical elements loom large.
In the marginalist approach, in contrast, output and distributive variables (the real wage and profits, which are part of the surplus and, thus, residual for surplus authors) are determined simultaneously by supply and demand. There is no space for alternative views on the determination of output or the real wage. Full employment (a version of Say's Law) is a necessary result with flexible prices (hence, rigidities are necessary to get unemployment).
Garegnani, P. (1984), “Value and Distribution in the Classical Economists and Marx,” Oxford Economic Papers, 36, pp. 291-325. Link here (subscription required).
PS: A complementary post, diagram and suggested reading at Robert Vienneau's Thoughts on Economics.