I think you are stating several important insights.
The word object in pragmatism and pragmatic semiotics has a much wider range of meanings than the extremely reductive sense of a “compact physical object”. Anyone wishing to explore the richness of its meaning could hardly do better than to sample the senses of the Greek pragma that imbue the Latin-derived object.
There is reason to think that the sense of the word object that means objective, purpose, target, intention, goal, end, aim, and so on is more fundamental than the more restrictive sense of a compact physical object. That is in fact one of the most critical insights that comes down to us from long lines of physical theory and also from the traditions known as “process thinking”, suggesting that our concepts of physical objects are derivative in relation to our concepts of process, since they arise from our ability to discover “invariants under transformations”, that is, the formal constructs that are preserved by the operations or processes that transform the states of a system.
As a general rule, we should avoid language that confuses signs and objects. In particular, referring to mental representations as “ideal objects” is just asking for trouble, and that on several counts, including the risk of confusing mental ideas with Platonic ideas. Language like that brings all the confusions of conceptualism, nominalism, and psychologism down on our heads.
Given that Peirce’s critique of Cartesian philosophy is of a piece with the rest of his thought, it does not seem wise to backslide on this score and reinfect semiotics with the dualisms that Peirce was so persistent in rooting out. For example, so far as the mind/body dualism goes, Peirce regarded the body as one of the first objects that a developing being would naturally “construct” from the flux of experience, that is, construe or conceptualize as an object from the impressions available in the stream of awareness. There is a potential misunderstanding that needs to be avoided here. It is not that noticing a dualism is a bad thing — where one is operative it cannot be denied. The important thing is — by the time one notices a dualism, one has already become a third party, a mediator, a synthetic operator, and so one must recognize that more than two components are already in play.