I would suggest that "the science of expressions" would primarily describe "semantics", the relations between words and symbols and that which they are used to "signify".

General semantics is much more, because it deals with a theory of how we process experiences to create meaning, including non-verbal and non-lexical "meaning". "Expressions" denotes only the "output process" - not even how it get produced.

So any "science of expressions" would, unless the expression is severely misused, indicate only the symbols and gestures we use to perform indications.

So general semantics is much more that a "science of expression", and it is also much more than "semantics".

Tarski and Chwistek both worked towards a formal semantic theory of language.

Footnote 3 on page xxix provides "metamathematics" as an alternative name or description for "rational semantics", and in doing so "identifies" "rational semantics" as a form of what is known as "model theory", an outgrowth of and very similar to Tarski's model for providing a semantic definition of "truth".

That provides strong corroborating evidence that "rational semantics" is not "general semantics", but is a relative of Tarski's work and its relatives dealing with model theory - langauages for describing relations between symbols and objects - philosophically "informing" our notion of "reference" and "representation".

To summarize.
No, general semantics is much more than "a science of expressions". A "science of expression" would be principally limited to the verbal levels of abstraction, and "rational semantics" to "formal" (mathemically) defined subsystems of such.

I would support Milton's somewhat colorful description of "dumbing down", but it's too weak - "ripping the guts out" would better describe how much is lost.

David wrote, "In my view, this revision of Ben's original offering extends the scope of the offering to include consideration of factors associated with "evaluation", "natural language", and the individual assignment of meaning to "semantic variables".

I'm inclined to feel that this still leaves much too little emphasis on the abstracting process, which is fundamental to general semantics. "Evaluating" has a strong connotation as a conscious process, whereas the vast majority of our abstracting taking place operates prior to consciousness of abstracting. We "retroactively" apply our "theory" of abstracting to "inform" what arrives in our counsciousness and make inferences about the source (when we practice consciousness of abstracting). We may then "evaluate" the verbalizations we abstract into, sometimes taking into consideration our model of abstracting using the structural differential as a model or using a more complex expansion thereof, but unless we are mathematically familiar with model theory, we probably do not evaluate our formulations taking into consideration metamathematics, "rational semantics", model theoy, etc.

So, I think even your proposed expansion of Ben's suggestion falls very far short of general semantics.