In harmony with DDS, you are caught up in a philosophically idealistic view of God that doesn't necessarily represent the real world. For example, God need not be omnipresent in the absolute sense to be an effective ruler and administer justice perfectly. Rather, He merely needs to have His hand on every particle of matter in the universe as to monitor and supervise it closely.
DDS evolved because most of the church fathers felt that God had to conform to THEIR philosophical ideals. They never stopped to ask themselves whether such a God isn't a contradiction in terms or contradicts the biblical data.
Let's take for example the topic you raised here - omnipresence. According to Charles Hodge, the orthodox view, which he accepted, is that God fills all space repletely/plenally. Thus the fullness of God is fully present at every point in space (as opposed to being more or less sparsely distributed, volumetrically, throughout space). This assumption flatly contradicts the biblical data. How so? It contradicts the notion of an outpouring of the Third Person. If God is already fully present everywhere, there is no meaningful sense in which He can translocate. In fact Jesus foretold Pentecost as trading places. Meaning, the Son would return to the throne and, in His stead, the Third person would descend down here. And that's precisely what happened. First we have the translocation of the Son - and it's a wholly physical event...
"After he said this, he was taken up before their very eyes, and a cloud hid him from their sight" (Acts 1)
...followed by the translocation of the Third Person, just one chapter later:
"They saw what seemed to be tongues of Fire that separated and came to rest on each of them.
4All of them were filled with the Holy [Wind]" (Acts 2).
Outpourings also contradict a 2nd facet of DDS - the claim that God is indivisible into parts. The concept of trading places indicates that God is divisible into parts. For example 120 separate tongues of Fire descended.
Again, 100% of the biblical data favors a material God. And indeed, if He is material, then your objection to Mormonism seems blunted, since two material objects cannot fully occupy the same space - thus something less than replete/plenal omnipresence is only to be expected.