[agalunar]

To my ears, there's a difference!

  I am watched.            (present passive)
  I was watched.           (past passive)
  I have been watched.     (present perfect passive)
  I had been watched.      (past perfect passive)

  I am being watched.      (present progressive passive)
  I was being watched.     (past progressive passive)
  I've been being watched. (present perfect progressive passive)
  I'd been being watched.  (past perfect progressive passive)

  I must be watched.
  I must have been watched.
  I must have been watched.
  I must have had been watched.

  I must be being watched.
  I must've been being watched.
  I must've been being watched.
  I must've had been being watched.

I think is roughly it? Although now I'm beginning to doubt myself, and maybe it is just:

  I must be watched.
  I must have been watched.
  I must have been watched.
  I must have been watched.

  I must be being watched.
  I must've been being watched.
  I must've been being watched.
  I must've been being watched.

or really, maybe it's better to say those forms don't exist:

  I must be watched.
  I must have been watched.
  —
  —

  I must be being watched.
  I must've been being watched.
  —
  —

What's neat is that I can assign meaning to "must've 'd been", but it really teeters on the edge, sometimes sounding strange but acceptable and sometimes sounding simply wrong.

I can't find many examples of it, but there are a few I've found online:

"To qualify for a special enrollment due to a permanent move, you must have had been enrolled in other minimum essential coverage, such as under a job-based health plan, another Marketplace plan, or Medicaid."

"Sales must have had been in the same year as the tax return."

So perhaps it's best to say it's nonstandard but attested.

[ickoonite]

Oh my. You have got yourself in quite a pickle. “Must have had been” is simply wrong; in your examples, it should always be “must have been”.

[agalunar]

> "Must have had been" is simply wrong; in your examples, it should always be "must have been".

As a matter of prescription, maybe, but as a matter of description? I think it's interesting. It is meaningful and it's something that English speakers produce. Here are other examples in the wild:

"To complete the request, the owner of the permit must have had been present at the time the citation was written, present a valid permit to the Tax Collector in person, have a copy of their citation, and pay a $7.50 processing fee to the Tax Collector if approved."

"Lankeshwar must have had been easy to defeat compared to new-age Ravanas."

It can even have a distinct meaning (rather than just being a variation), which is how I would interpret it. Which I think is cool.

It's perfectly fine to say "don't use this construction if you want to be taken seriously by so-and-so", but if its usage happens to be dialectal, for example, I don't think you can say those speakers are using their dialect of English incorrectly.