New way of understanding the present perfect tense
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
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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.
Your attempt doesn't work. You say
The past participle together with the corresponding object (e.g. "done homework") is a property of this object which was obtained in the past.
That would not explain intransitive verbs. For example:
John: There are seats available. Why are you standing rather than sitting?
Jane: Because I have always stood.
What is the object of 'stood' in that case?
Answer
Unfortunately your theory is incorrect.
Discussion
In English the following have different meanings.
A.
"John, have you done your homework?"
"Yes, I have done my homework." [I finished my homework.]
B.
"John, do you have your homework done?"
"Yes, I have my homework done." [I have my homework in a state of completion]
The latter version approximates to your idea. However the latter version is not an example of present perfect.
I sympathize with your struggles. As a teacher, I face this question almost daily when helping my students understand and use present perfect in a more natural way. This comes up frequently when helping them write emails to their colleagues all over the world. What I have found, is the following:
1) Usage of present perfect and it's accompanying logic seems to be cultural as well as regional. Because of this, there is no "logic" with it's use. "My mom always said that so I guess that's why I say it." or "That's what we say in [fill in the country of your choice.]"
2) Native speakers themselves often don't know why they use / used a present perfect construction, and when they do explain why, that explanation is situational rather than comprehensive.
3) Language teaching books always simplify things or pick artificial situations to "explain" present perfect, and these sentences are usually isolated in context and can be explained in other ways besides the explanation given. Some books are better than others.
4) Because simple past and present perfect are so closely related, native speakers will always be able to substitute one for the other and give a completely reasonable argument in favor of their substitution. Also, non-native speakers will be able to give reasons justifying their use which will often stump the teacher or seem completely reasonable.
and finally,
5) Use of the present perfect is highly personal. One person will respond upon being asked "Where's the milk I put in the office fridge?" with "I've finished it." whereas another will say "I finished it." Or, "Did you do your homework?" with "I've done my homework." or "I did my homework." And applying observation 4, equally valid and "airtight" explanations can be given as to why one should be used over the other.
To put 5 in perspective, I recently assigned my students the task of writing a bill collection email from a package shipping company. Most of the letters started this way: Dear Customer, Our company has recently delivered your orders but we did not receive payment. I have also called you twice to ask about payment but I have not received a reply. I am writing to ask for payment because I have not received it." I asked the class why they used present perfect and they said because they did these things in the past but they all affect the present. I gave my reasons why the simple past was a better choice. Some agreed, others gave reasons why present perfect was better. A fellow teacher commented that he saw nothing wrong. He's from Australia and in conversation, I notice he uses present perfect for things I'm pretty sure I would use simple past.
So, in a nutshell, what I'm saying is to not feel frustrated with present perfect. Continue to think about it. Find your own answers that help you to be more "accurate." I know some are going to complain about this point of view but I would suggest that you find your own style that fits in with the generally accepted PP rules. To liken this to quantum mechanics; sometimes it's a wave and sometimes it's a particle, but it's always both at the same time.