The OP offers one side of the discussion (actually, many discussions) around the polysemous word, ἁρπαγμός. It is well understood to have two meanings. It's commonly known verbs can have active and passive senses. However, some nouns can exhibit these two senses, too. The lexical semantics of the word ἁρπαγμός define it as being one such word.
- To rapidly seize (as the OP has noted) [active sense]
- To tenaciously hold on to [passive sense]
With a little thought, one can see the strong relationship between these two meanings; but, one is active, the other passive.
Now, that highlights the problem. One can't resolve the Trinitarian question by a focus on a lexical solution. The word has two meanings. So, how does one resolve that?
First an illustration.
A house has a structure. That is, the elements within the structure have relationships with the house and with each other. The larger house structure defines the structure of the smaller rooms within it. If the bathroom door opens into the den, that door can't also open into the kitchen. Those rooms, in turn, define the structure and constrain the relationships between the elements within each room, that is, the furniture. And so on. The toilet paper is next to the toilet, it's not on the shelf in the living room. Just like form and function work together, so the detailed elements within a larger structure work together. Coherency rules.
Texts work the same way. While one could actually make "toilet paper on a living room shelf" work (with a little planning), no one would opt for such a complex solution. Simpler solutions (aka Occam's Razor) provide the sensible, rational results. The elements of a text work just like toilet paper placement. It's much more coherent to relate the toilet paper to the larger elements via a defined relationship to the toilet. To make this obvious, no one who sees a roll of toilet paper on the living room shelf would immediately think that means to be used in the bathroom. The toilet paper on the shelf has different meaning than the toilet paper next to the toilet. The relationship defines.
In other words, to resolve a lexical problem (toilet paper placement), you examine the large semantic elements (the function of the rooms). One can't just examine the toilet paper. Consideration must be given to the cohesive properties of the larger structures.
Now, with that illustration and metaphor in mind:
Philippians 2:6-11 is a well known poem, structured as a chiasmus. Anyone can see this quite easily since the semantic content of the poem starts and ends with exalted elements and the center is highly debased. In fact the exact center is the genitive phrase, θανάτου δὲ σταυροῦ ("a cross kind of death"). From beginning to middle and middle to end there's a staircase leading down and then one leading back up. The chiastic structure is clearly there.
This structure fixes in place certain details and, more importantly, cohesive relationships between those details. The center is prominent and the beginning and end directly relate to each other. This forces certain semantic correlations. These correlates constrain interpretation of the respective elements. Just like the toilet paper is next to the toilet, the architect of the text has placed the crucifixion in the focused middle, and has placed the exaltation at the beginning and the end. This is very standard, typical chiastic form: A relates to A', B to B', and so on. See this page for more information about chiasma.
So, let's make the OP's assumption: Jesus is a god (a demigod of some sort). This assumption presents an immediate conflict within the poem because of the structure of the poem.
There are two expressions used in the second half of the poem:
bestowed on Him the name which is above every name,
This is the name above every name. What name is that? Or, more importantly, whose name is that. In ancient cultures (as opposed to our modern one), name identified the person. That is, it brought to the forefront the who that person is. It wasn't just a label on the front of their shirt. In this case, this person is identified as a person who is above every other person. There is only one person who is that. God. The only other possibility is the logical contradiction of a person being above God. That person, by definition, would be God.
Question then: How does this relate to the demigod at the beginning of the poem?
Next:
so that at the name of Jesus every knee will bow, of those who are in
heaven and on earth and under the earth,
And the poem, lest the point be misunderstood, goes even further to reinforce the extent of this exaltation. Every knee will bow! How is the set of persons defined who bow? Is it just human beings? No! The set is composed of every single being, without exception, that was (and is, and will be) ever created--"of those who are in heaven and on earth and under the earth." If the being has knees, that being bows in worship. No exceptions.
And the text is very explicit, re-announcing that this person is Jesus. There's no doubt left by the text as to who is being referred to.
Question then: How does this relate to the demigod at the beginning of the poem?
I see only three answers.
- One has to admit that the demigod announced at the beginning of the poem has now, at the end of the poem, been exalted into the position of being the one and only God. This alternative is more difficult to explain than the Trinitarian position. It's some kind of diastatic transcendence. One is going to have to go to a lot of effort to explain this new theological doctrine.
- One has to become a pantheist. If the exalted person is to be worshiped as a God, and there is already a God (the Father), then one must now accept that there is now an additional God. And this must not be a demigod, but an actual God. Pantheism is the only alternative. In this case one has ironically forfeited one's non-trinitarian position for pantheism (non-trinitarianism being an extremely strong form of monotheism).
And the third:
A better explanation is that this exaltation mirrors the beginning of the poem. Jesus let go of the "form of God." That is, he let go of that which makes God transcendent as God. He transcended his transcendence and became immanent. This immanence is then transformed back into transcendence in the glorification of Christ.
The form of God, mentioned at the beginning of the poem, that is, the transcendence of God, is mirrored in the poem by its opening and closing statements. How? In typical chiastic form:
He already existed in the form of God
mirrors
the glory of God the Father.
'Form' and 'glory', while certainly not synonymous, share a common lexical component of 'visibility'. The transcendence, in order to make it graspable, is described as 'form'. How else could one label it? And so, it is let go. The end result, after the crucifixion, is to exalt back into the transcendence of God and into full glory.
So, the problem, presented by the structure of the text, is that if one makes the OP's assumption, and if one wants to remain a monotheist, then one also has to explain how Jesus became God.
The text is written to constrain to only one solution.