As you and others here have said, your CRA reply is essentially the most common one, the Systems Reply. But your statement misses some important aspects, such as Searle's point about formal symbol manipulation, which is the one thing his CRA gets right. To understand how both things can be right: lack of semantics at the Searle-computer level and the potential for understanding at the CR-system level, one should understand the relationships among the Searle-computer and its two kinds of input.
The Chinese Room's heat source is the fact that it produces two levels of Turing computation, both of which are processing the Chinese symbols. Level-1 is Searle himself, acting as a UTM-computer (a universal Turing machine; like a CPU). Level-2 is "the system" whose computation of the Chinese is determined solely by the program and its execution configuration (memory, state, etc.). Note that the existence of the two computations is a fact, not as in "I'm stating my opinion as a fact", but as in "it is an objective mathematical fact, like the Pythagorean Theorem, which anyone can understand and verify for themself".
Searle's self-consciousness is a kind of 3rd level of "information processing" (which might or might not be a computation). It allows him to introspect on his own level-1 universal computation. But he cannot similarly introspect on the level-2 computation. For level-2, the Searle-UTM is merely its physical substrate, analogous to a person's neuron-level, not their consciousness-level. Thus, the Searle-UTM never knows what his program is doing, whether it is doing a Turing Test or taxes or tic-tac-toe.
Also note that the Searle-UTM is processing two classes of symbols: #1 the English symbols of the program, which people always ignore, and #2 the Chinese symbols, which captivate people like shiny objects. Thus, to correctly address "symbol manipulation in the CR", one must fully address the three symbol-processing relationships:
the level-1 relationship: Searle-UTM to the English program symbols (#1),
the level-1 relationship: Searle-UTM to Chinese symbols (#2), and
the level-2 relationship: the program's computation to the Chinese symbols (#2).
In the CRA, Searle only addresses the 2nd relationship: his own UTM processing of the Chinese (#2), which he correctly characterizes as formal symbol manipulation, i.e,. syntactic and meaningless or non-intentional to him. Your reply above does not account for this 2nd relationship. For when you speak of manipulating English symbols in your mind, the key difference is that your mind can interpret them, whereas the Searle-UTM cannot itself interpret the Chinese symbols. That's Searle's main point, and he is correct about that much of it. (His mistake lies in missing the other aspects of the two computations.)
Virtually no one addresses the 1st relationship. However, clearly the Searle-UTM must process the program symbols with some level of semantic intentionality.* That is why they must be in English! This fact alone contradicts Searle's own CRA conclusions.
Most importantly, the 3rd relationship is approximately the famous Systems Reply, as mentioned. Searle tries to dismiss the Systems Reply, and apparently people are left to decide for themselves whether they agree, disagree, or prefer to focus on some other aspect of the CRA or science fiction or philosophy, etc.
But the key point about the Systems Reply is this: although Searle cannot discern it, the additional level-2 computation is not merely some philosophical assertion. It is a mathematical fact about how Turing computation works. A universal computation on its #1 program input and its #2 nominal input, instantiates the program's own distinct TM computation on the nominal input. Period. Trying to rebut this would be like trying to rebut the Pythagorean Theorem.
The slight difference here with the usual Systems Reply is that one cannot further assume that the Turing Test is valid. The CR's external behavior does not prove that the program's algorithm is equivalent to a human's internal understanding of the Chinese. But the CRA does not disprove it, so it remains an open possibility. Presumably, that is why over the years Searle has evolved his critique to more properly address computation in general, rather than just the CRA's focus on universal programmability.
* Obviously, full blown self-conscious intentionality is not required for computers, but translating a program's symbolic references into physical entities, actions, and events is required. That goes beyond formal symbol manipulation into enacting non-formal associations.
Ref (and see refs therein): Refuting Searle's "syntax is not semantics" argument.
