I must gently disagree with your assertion that “conversion” is neutral as a substitute for “apostasy”. If the latter is indeed negative for what it refers to (the unambiguous rejection of a particular religious faith), then the former is indeed more positive for those of a pro-religion bent, because it’s about exchanging one religion for another. For that matter, an apostate isn’t necessarily agnostic or atheist. I’m a Presbyterian apostate because I rejected P’ianism, the church I was raised in (as opposed to being born into). If I become a Buddhist tomorrow, I’d still be a P’ian apostate, although I should think in most contexts my new embrace of another faith would take classificatory preeminence.
To be frank, I and other ex-whatevers can attempt consciousness-raising and call ourselves apostates until we’re blue in the face, but the term will still bear negative connotations for most people, due mostly to the RCC’s historic imperative of persecuting and executing people for, among other things, apostasy – as do certain Wahhabist Islamic nations today, to citizens who’ve renounced Islam, whether they’ve taken up another religion or not. Perhaps a term like “renunciate” (someone who has renounced) could better serve as a value-neutral and largely ahistoric substitute for “apostate,” but my dictionary doesn’t list the term.
I have another problem with the traditional (racialist) definition of Jewish in the context of the OP, which asked how we should refer to a Jew’s abandonment of his religious identity. It seems to me the OP takes it as a given that the hypothetical ex-Jew is no longer Jewish, at least in all ways that he is able to determine for himself (i.e., in every way but the genetic or racial sense). Therefore the argument that Isaac Cohen (by any other name) will always be a Jew whether he likes it or not, unless he actively converts to another faith (and even then it’s debatable), is begging the question somewhat.
But the OP should be clearer on Isaac Cohen’s relationship to his [former?] faith – is he merely lapsed (but still a believer), or does he disbelieve the religious creeds of Judaism? Is he simply not religious anymore (in which case he probably doesn’t qualify as an apostate), or does he consider himself an agnostic or atheist (or something else)?