We're discussing the distinction, sure, but is each of us distinguishing the other's statements about implicature from the other's implications about implicature?

No, because we do not need to. We are responding to what we perceive the others' meanings to be, regardless of how explicitly they were expressed. Only if we are are uncertain of an implication, or if one person perceives an implication that another did not intend, do we need to raise the issue.

If I read this thread, then attempt to write down a list of significant statements you made from memory, and then compare that list to your actual text; will it contain things you did not say?

Yes. This will still be the case if you do not do this from memory, but write out a paraphrase with the original text in front of you.

Will it also contain things that I thought followed from what you said, but that you neither said nor meant?

It may well do that as well. Communication is fallible. That is why it has to be a two-way process: fire and forget doesn't work. Hence also such devices as the ideological Turing test: formulating someone else's views on a subject in a way that they agree is accurate.

ETA: The university library has the Clark & Clark book. Kahnemann and Tversky don't give a page reference, but chapters 2 and 3 of C&C discuss implicatures. What I gather from it is that yes, people make them. In experiments, their memories of a text are influenced in various ways by the background knowledge that they bring to bear. Incongruous details are more often forgotten, while congruous but absent details are added in retelling. The experiments cited in Clark & Clark measure things like how long certain linguistic comprehension tasks take and what errors are made. These are compared with the predictions of various models of how the brain is processing things.

Sounds like Bayesian updating to me, with the evidence received (the text) not being so strong as to screen off the priors. But unless you are specifically attending to it (as you might well be doing, e.g. when examining a witness at a trial) all you are aware of is the result.

I found that surprising, enlightening, and scary.

Welcome to consciousness of abstraction! Your brain does not distinguish true beliefs from false beliefs!