Learn English – Grammar of present perfect continous of sit and stand

I wouldn't be too surprised if the first two are examples of the same sort of "misheard->misspelled" transitions that result in a lot of younger people thinking that "should of been" is a valid construction; I could totally see how someone could go from hearing "he has been" and "he's been" to thinking that "he is been" is what was actually said.

However, all three of your initial examples are bad grammar and should be avoided; your suggested versions are correct.

As far as it goes, your model is correct. What it depicts, in fact, is what many authorities regard as the historical origin of the perfect construction in utterances of the sort chasly from UK instances:

I have my homework finished = I have my homework in a finished state

• The standard argument is that this sort of utterance became grammaticalized in very much the same way that the periphrastic modal have to/hafta was grammaticalized from utterances of this sort:

  I still have my homework to do → I still have to do my homework

Do note that, as chasly from UK cogently points out, utterances of this sort are not restricted to the narrow sense "possession"; other senses of lexical HAVE may be involved. For instance

Now that we have that problem disposed of ... to have a problem means that we are presented with the problem, not that we possess the problem

And your device of treating the two components of the construction—the HAVE form and the participle—as bearers of distinct sorts of information is to my mind a happy one for pedagogic purposes. (In fact, I have adopted it myself in my discussion of the Grammatical meaning of the construction over on ell.SE.) It is not strictly true—the 'meaning' of the construction derives from the collocation, not from the atomic meanings of its parts—but it does point up the peculiar character of the English perfect: it designates a state current at reference time which arises out of a prior eventuality. And it makes it very easy to explain the "present perfect puzzle"^†: why the PrPf is not used with temporal expressions which do not include the present.

Where your model falls down is in failing to account for a number of uses to which the perfect construction has been extended since its origin in the dark backward and abysm of Old English. What you describe is the resultative or stative perfect; but there are also existential or experiential perfects ("I have often visited Paris") and continuative or universal perfects ("I have been living here since 1976"). I don't think your model will accommodate these.

(The paper by James McCawley which introduced these distinctions in 1971 also offered a Hot News perfect—"I've just won the Nobel prize!"—but this is now regarded as a special instance of existential or resultative perfects, and McCawley himself withdrew the category in 1981.)

Grammarians have been arguing about just what the perfect "means" for forty-some-odd years now. In my opinion, the most useful recent treatment is that laid out by Atsuko Nishiyama and Jean-Pierre Koenig in a series of papers culminating in “What is a perfect state?”, Language 86, 3, 2010. Nishiyama and Koenig turn their attention to the pragmatics of the perfect and conclude that

the perfect is pragmatically, rather than semantically, ambiguous. The meaning of the perfect introduces a base eventuality and a perfect state whose category is underspecified semantically. Neo-Gricean reasoning leads the hearers to appropriately fill in the value of that variable.

An earlier version of their paper is available online here, but it's formidably technical; I try to make its conclusions intelligible at §3.2 Pragmatic meaning of my post on perfects at ell.SE.

^† _{Named by Wolfgang Klein in 'The present perfect puzzle', Language 68 (1992), 525–552. See also Anita Mittwoch, “The purported Present Perfect Puzzle”, in D. Gorland et al. (eds), Meaning and Grammar of Nouns and Verbs, 2014.}