Actually, I think your examples are a blend of oxymoron and the form of understatement called litotes, which negates the negative to create a positive. Some examples:
There was no small crowd at the accident site.
The engineers in Silicon Valley showed no little interest in the new invention.
Dr. Black's diagnostic skills may not have been the best, but neither were they insignificant.
The roller coaster ride gave me a small, but not inconsequential, thrill.
With no small effort, I could probably turn some of your examples into litotes. Let's see . . ..
Yours: "What the problem isn't, is that they're too attentive."
Mine: The problem is they are not the least bit inattentive. [In other words, they don't miss a trick!]
Yours: "What the problem is, isn't that they're too attentive."
Mine: The problem is not from their lack of inattentiveness.
Yours: "What the problem isn't, isn't that they're too attentive."
Mine: That they are not inattentive is not the problem, but that they are in fact inattentive.
Frankly, I think your examples--particularly the last one--also resemble a truncated form of periphrasis; that is, beating around the bush and not getting to the point. There is a time and place even for periphrasis, particularly in a delicate situation in which diplomacy is not unimportant. Nevertheless, an over-dependence on periphrasis confuse and even alienate your audience.
If delicacy is the purpose of using your examples, then fine. If not, you are simply engaging in word play and perhaps attempting to push the envelope of irony inelegantly. To craft a more elegant irony, you might toy with Kirkegaard's concept of "infinite, absolute negativity" (it might be "infinite, absolute negativity"). For example, the frog and the scorpion:
One day at the creek's edge, a scorpion asks a frog if he would transport him to the other side of the creek. The frog experiences no small amount of fear and trepidation, even when the scorpion promises the frog that he'll not only not string him but additionally he'll show Mr. Frog where a huge swarm of flies hangs out on the other side of the creek if he will only give him a ride.
The frog thinks to himself, "Hmmm. Mr. Scorpion has promised not to sting me, and those flies would surely taste good at this point, as I'm really kind of hungry. On the other hand, what if he wants me to think that he's sincere when in fact he isn't sincere and simply wants to sting me. No, I think he's using reverse psychology on me, and he wants me to think he's insincere but is only pretending to be insincere about his insincerity, so that I'll actually think he's sincere. No, that can't be right. Maybe . . .."
And so it goes. Mr. Frog is overthinking things, and he should have trusted his initial instinct that Mr. Scorpion could not be trusted. Period.