Apophasis (ə-pŏf′ə-sĭs) comes in different guises: some ethical, some unethical, and some a mixture of both ethical and unethical elements. I think your examples comprise the latter; namely, an admixture of--or cross between--the two. Here are three instances of apophasis: one ethical, one unethical, and one an admixture:
I need not mention our honoree's three purple hearts, two medals of valor, and the presidential medal of freedom, because we are here today to honor his leadership in the nationwide effort to eradicate hunger in America.
I won't even touch on the candidate's many scrapes with the law in his 20s and his pleading "no contest" to a charge of embezzlement in his 30s. To do that would be unfair of me and might prejudice you, the voters, which is something I would not want to do.
Not to encourage you to have doubts about my competitor's qualifications, but what about the Bennett Poll in which 86 percent of those polled insisted that my competitor has fudged his resume?
On its face, the last exemplar seems to be purely unethical, since the speaker is doing what he said he would not do. In other words, he lies. On the other hand, are there not situations in which an issue has not been fully resolved and consequently needs to brought back into the public spotlight and debated once again? If that pertains, then encouraging an audience to have doubts about the competitor might be the ethical thing to do.
If in fact the rhetor is simply stirring the pot for his own devious purposes, knowing full well that the results of the Bennett Poll were discredited long ago, then he is clearly being unethical. Put differently, if he is in fact beating a dead horse, then shame on him! He will accomplish very little of value and perhaps succeed only in turning people against him for wasting their time by rehashing old and settled business.
In conclusion, each rhetorical figure and trope can potentially be tinged with elements of another figure or trope. We may treat apophasis, for example, as a theoretically singular figure of speech, but in practice it can take on elements of other figures. Delivered ironically, apophasis is no longer just an apophasis but something else entirely--a horse of a different color, so to speak.
For the time being, your initial thought that "apophasis is almost right" is spot on. Your examples comprise simply a "variation on the theme."