Jim,
A fatal problem with your reasoning imo is that you still have not defined what a "person" is, (1) in common usage and (2) as a technical term of trinitarian theology (i.e. as a fixed equivalent of Greek hupostasis and Latin persona). You seem to assume that definitions # 1 and 2 are identical, which I doubt.
But let us stay with # 1 for a little while. In general usage, a "person" is an individual of the human species -- in opposition to "things" or "animals". If we call God, angels or aliens "persons" we do so in a derived sense, by extrapolating human characteristics (e.g. life, language, consciousness, intelligence, feelings, memory and will) to other beings. It is analogical thinking -- one of the most blatant cases of anthropomorphism and anthropocentrism: we would call a "person" any potential being we would deem to be like us enough.
The personality ascribed to "God" in monotheism (and before that to the gods and goddesses of polytheism) is unseparable from anthropomorphical speech in theology and mythology. Monotheism taught us to dismiss the corporeal anthropomorphisms about "God" as mere figures of speech (Yhwh's "arms," "hands," "fingers," "nose," "mouth," "eyes," "feet" etc.) but to retain the "intellectual" or "moral" ones as somehow "literal": God's "will," "memory," "word," "wisdom," "love" or "hate" are not considered as metaphors. This is quite arbitrary if you think of it but never mind. Let's assume "God" and "angels" are "persons" -- morally human-like, corporally non-human-like, non-humans.
So "God" and "angels" -- "persons" by this somewhat painful definition -- are called "spirits". From this you seem to jump to the conclusion that the word "spirit" means or implies "person"! All you can really conclude from this premise (fwiw) is that a "person" can be called "a spirit," or "a spirit" can be "a person". Whether it can only be a "person" is a quite different matter. When the Bible speaks of people's (human) spirits does that mean a person within the person? What about the animals' "spirits" which are generated by God's "spirit" in Psalm 104 for instance?
Qualifying "God" as "spirit" is definitely not qualifying him as a person -- this task is done by our selective acceptation of anthropomorphisms: God is not a person because he is called a "spirit," he is a person because we ascribe him life, intelligence, will, feelings, etc.
As you know the main antithesis to "spirit" in the Bible is not "thing" but "flesh". "God is a spirit" tells us strictly nothing about his "personality" but means he is not fleshly, material or physical. That's about all. And stepping back (semantically) it is almost the opposite. When I call God a "person" I suggest he is somehow "like me"; when I call him a "spirit" I affirm he is "not like me".
So what about the NT "Holy Spirit"? Is it "something" or "someone"? To answer that question we should consider all NT uses of pneuma (neuter); the obvious conclusion would be that "personal" or "anthropomorphical" suggestions are the exception (mostly limited to Acts) rather than the rule. That doesn't mean they should be explained away (although, as I said and maintain, the personification of Wisdom in Luke, where it has no obvious christological nor pneumatological role, should incline the reader to caution). But even we should conclude that some NT texts treat the Holy Spirit as a "person-like-us" that would not warrant reading this representation into the rest of the NT.
Let me add (once more) that admitting that, by and large, the NT doesn't depart too much from the overwhelmingly impersonal use of to pneuma in Greek doesn't rule out considering the Holy Spirit as a divine hupostasis (a very abstract term) or persona (the comedian mask, hence role or character) by Trinitarian definitions. Those are not about persons in the ordinary sense, but divine "dimensions" or "modes of being" (Karl Barth). What if the word pneuma's resistance to anthropomorphism was precisely helpful to remind that "God" cannot be reduced to the anthropomorphical notion of "person" -- being ultimately both personal and impersonal?