I can go with that.Agree with the sentence before the word agree!
God is omnipresent, I thought you held that view too.
If you are to see Oneness Christology, we need to agree to the basics. In your "tapestry" that you described you didn't hold to these basics and so you misstated the Oneness position.
Once we have the Biblical basics, understand that at the incarnation, God's nature didn't change or transform. There was an addition to how God existed as a genuine man, but NOT a taking away or transforming of the nature of God.
Here to summarize:
Everywhere Present – Jeremiah 23:24; Acts 17:27-28
Invisible – 1 Timothy 6:16
Eternal past and future – 1 Timothy 1:17
Immutable (unchanging) – Malachi 3:6
All knowing (omniscient) – Psalm 139:1-6
Trinitarians have and should agree with this because it is simply the nature of God as described in the Bible. It is important that when we talk about Christology, these fundamental truths of the Bible don't change. That's not so hard. This is not a trick. My point is that Oneness theology has it's foundation in these very basic Biblical principles of God's nature. There shouldn't be anything controversial about anything I've said above.
But add,the being called God who had three centers of self consciousness possesses the attributes of God and the three centers of self consciousness fully share the being called God. Therefore those attributes also ascribe to the three centers of self consciousness.