"While, on the surface," Comma Question

I understand most comma rules, but this one stumps me. It is my understanding that the sentence should still make sense after taking out the X in "..., [X], ...." As an example: My friend, a hard-worker, would be a great fit for your company.

I've seen examples like the following before, but these don't seem to abide by that rule. Are they grammatically incorrect, or are they exceptions?

1. While, on the surface, the plan looks executable, in practice, this is not so much the case.

2. While on the surface, the plan looks executable, in practice, this is not so much the case.

1. He claims to value his constituents, but in reality, this is not true.

2. He claims to value his constituents, while in reality, enacting policies that run counter to their interests.

The first example is not an exception to that rule, but the sentence has two offset clauses:

"While [...] the plan looks executable [...] this is not so much the case."

In the second example the second comma is not necessary:

"He claims to value his constituents, while in reality enacting policies that run counter to their interests."

I understand most comma rules, ...

Most comma rules are wrong, so this is not really a benefit. Commas are hard to use, and there is no perfect way because everybody reads them after their own reading and writing habits. And there are as many of them as there are of readers. The best comma rule is If you hear it, you write it. As a corollary, if you don't hear it, you don't write it. So you have to be listening. This is language.

Unlike spoken language, which co-evolved with us for over a million years, humans have no evolutionary history involving written language; literacy is modern technology, even younger than agriculture and horsemanship. And there are a lot of ways to do it, like Chinese characters (e.g, 墨) versus Pinyin (e.g, mò).

Consequently, there are lots of parts of language that don't fit well into writing, and are therefore mostly ignored. Intonation is one such; every utterance in every language has a tone contour, because every sound occurs at some pitch, and each sound in an utterance is followed by another. So we are making music at the same time we are making words; whether we want to or not.

Take that last sentence I just wrote, boldfaced above. I put a semicolon before the last clause to indicate the intonation, but others might have used a comma. Neither one of them (as I hear them, at least) is exactly what I want the sentence to sound like (and which I can hear, in my mind's ear). There are probably hundreds of significant intonational cues that could be represented by punctuation or something, but these are the two choices available and I picked one.

What a comma usually represents is a rhythmic cyclic change in intonation -- a sine wave -- roughly,

• mid - lo - mid - hi - mid
  repeated and stretchable over a few syllables, as in counting:

• ... seventy-two, seventy-three, seventy-four, seventy-five, seventy-six, ...

That's not quite that intonation I wanted before that last clause; but a full stop, which is what a semicolon provides, is even less appropriate.

In that last clause of the boldfaced sentence, I omitted a comma, too. There could have been a comma between whether we want to and or not. It's short and it's predictable, so I preferred to omit the comma, which means not hearing it. That's OK with me (the author), and I'm the only one I have to satisfy. But if I had used it, that would have been OK with me, too, since I could have pronounced it or not; there's no meaning difference in using comma intonation or not.

(this is, parenthetically, why all the grammatically-based rules for comma usage are wrong -- commas don't indicate anything grammatical in a sentence; rather, they attempt to indicate its intonation, which often highlights grammar, but is never controlled by it.)

That's what we humans always do with technology that doesn't work the way we'd like.
We cope; we develop workarounds; we tell stories; we complain. We go on.