Native English speaker here, with training in linguistics, and several other languages under my belt over the years.

In my native dialect, statements including "had to have been being" are rather common. My friends, family, co-workers, etc. use them regularly. In fact, I recall saying "he'd have had to have been being reckless" just earlier today. All five of the other people present- both immediate family and non-relatives from this area- knew precisely what was meant. In other words, that intimidating clump of verbs passed unremarked.

Further, to andensande's point, one might be inclined to replace that god-awful monstrosity with something like "he must've been reckless." To do so would be to wipe out some subtleties of meaning from the original. A replacement like "he must've been acting recklessly at the time" feels like the same general meaning to me, but it also sounds stuffy and snobbish in tone (for all that it's probably a much more effective construction).

All things considered, every language that I've ever dealt with in any capacity has had its share of peculiarities. In hindsight, however, I don't recall Arabic, Zulu, or even Gallo-Lati... er, I mean French... having quite as few peculiarities as my sponge-like mother tongue.

I could see saying "she'd had to have been watched" or "they had to have been watching her". Both sound very natural to my ear. Observed to me feels more like they're looking at every minute detail with some emotional distance and maybe a feeling of something novel. A scientist observes a rare bug walking on a leaf. A psychiatrist observes his patients' behaviors. It's maybe a more scientific and heavily detail-oriented form of watching. But a would-be abductor would be watching his victim. He may observe their habits, but that's while he's watching them. It's a very fine line and I'm sure that other native speakers would disagree. But for me, "observe" would feel out of place here.

“Had to have been kidding” is a relatively common phrase.

Very common and feels very natural to me. "You have to be kidding me" "He had to have been kidding" "He had to have been kidding me" or the rougher "he had to have been fucking with me" and "he must have been fucking with me" although "must have", of course, implies more certainty than "had to have". What a wonderfully subtle and complex language we have.

"to be ing", "was ing", and "will be *ing" if I remember correctly, are actually thought to be an early borrowing of celtic grammar. Not much celtic anything was adopted into English, but there's a possibility that this sentence structure may be one of the few contributions of the celtic languages that were displaced by germanic Anglo-Saxon languages that eventually formed English.

You can gloss it with 'under observation' I think fairly well. But the problem with

(1) She would have had to have been observed.

is that it misses out the gerund form preceding 'observed', which alters the meaning slightly in my opinion. It's difficult to get at precisely but I feel like the original sentence has a feeling of time-boundedness around when she was observed which you don't get without that gerund. I think?

(native speaker) I agree.

The original with "been being watched" feels like something the detective says when he first discovers the fact about watching. It has an exclamative aspect to it. There's a present sense of realization, mixed with the past sense of when the watching had taken place.

"She would have had to have been observed." is something like a lawyers distillation of what happened later for the court.

Trying to translate in French, I came up first with "Il eût fallu qu'elle eût été surveillée", but mostly because of morphological similarity (it's almost the same amount of verbs, right?). It's also just a more literary form of the simpler "Il aurait fallu qu'elle soit surveillée".

That being said, I have trouble to parse the original english sentence so I may be missing subtleties.

Or just “il fallait qu’elle soit surveillée.”