I agree with your statements generally.

I just reread some of the Cappadocians last night.  It reinforced my
concept that the whole "three persons with one substance" is really
not as important as most people think it is.  It leads people into
trying to figure out what the difference between person and substance
is, thus resulting in one of the postings last night, which was just
plain wrong.  It turns the Trinity into discussions about how 3 = 1.
In fact ousia and hypostatis were originally synonyms.  They came to
take on diffferent meanings in the specific context, but I don't think
there was ever a very clear definition of what the meanings were.  I
think both sides got suckered into using technical language that
simply didn't fit the situation very well.  The problem is that if you
push their argument too far you end up claiming that the same problem
exists for 3 people as the three persons.  With three people you also
have a single human substance and three individuals.  So why do you
say you have three people, but not three Gods?

After pages of what I think is basic gibberish, you come to the crux
of the matter: "substance" means a different thing when applied to
people than when applied to God.  The essense of being human is
fitting a certain form.  There can be many humans.  But the essense of
being God is a action: God is creator, redeemer, etc.  It's not a
universal of which there can be multiple exemplars.

What they end up saying is that the three persons form one God because
of the way they are interrelated.  With three people you have three
self-contained entities, each a person.  With God, you don't: God's
wisdom is the logos, the Son.  God's spirit is the holy spirit, the
Spirit.  All three are involved in everything God does.  It's not just
that they all discuss things and agree.  It's that all three persons
are essential to God's doing anything at all, just as our brain,
muscles, etc., are all required to do anything we do.

I claim that what's really sitting below the surface here is in fact a
very modern and sophisticated analysis of what it means to be a
person.  It's clear that in some sense the way we analyze things is
arbitrary.  At one level of analysis, cells are individual objects.
At another level it's molecules.  At a higher level it is people.  But
if we have two people next to each other, we always define the two
objects as the two people, rather than for example the left halves of
both of them being one object and the right halves of both being a
second object.  At whatever level of analysis we're working, we divide
things according to the way they interact: there's a lot more
interaction within a person than between the person and his
environment.  If things didn't come in "clumps", with more interaction
inside the clumps than between them, the whole concept of discrete
objects wouldn't be useful.  In this context, I think what's being
said is that the interaction among the three persons is tight enough
that at the highest level of analysis it makes sense to think of them
as a single God.  The things that makes God God involve all of them
working together as a whole, rather than each of them individually.

However at a more detailed level of analysis, we can see distinct
Father, Son, and Holy Spirit, and we can see an interpersonal
relationship among them.  This interpersonal relationship looks a lot
like the love that exists among humans.  Indeed it is the model for
that love.  If you take John and Paul seriously, our love is not an
independent thing, but a participation in this divine love.  Thus at
this level of analysis it makes sense to speak of distinct persons.

Frankly, the simplest thing would be to say either that Father, Son
and Holy Spirit are each part of God, or conversely to say that God is
a composite entity made up of Father, Son, and Holy Spirit.  However
Christian theologians have generally not wanted to speak of the
persons as simply parts of God.  I think the refusal to use this
language is a mistake.  It's true that we'd be using "part" in a
slightly non-standard way.  But God is enough different than we are
that any words we use are going to be used slightly differently.  The
fact is, it's a pretty good starting point.  The reason it's not quite
right is that parts are defined by physical boundaries.  This may be
appropriate for LDS belief, and may actually be the most significant
difference between LDS and orthodox beliefs on the Trinity.  But in
orthodox belief, Father, Son, and Holy Spirit are all omnipresent, so
you can't draw a physical boundary between them.  They're in the same
"place".  They differ not in location but in "mode".  

Here the explanations are slightly different in East and West, but I
think mean the same thing.  Father, Son, and Holy Spirit are different
"modes of existence".  The Father is uncreated, the origin and lover.
The Son is begotten from the Father, the obedient son, and the word of
God.  The Holy Spirit proceeds from the Father to the Son.  It's as if
you had the distinction you'd normally expect between a father and
son, but without any physical separation of the distinct entities as
separate pieces.  And the persons are differently related than a
normal father and son, because instead of being three instances of a
single class, they each have different roles that are essential for
God to do what he does (sort of as if there were a personal
relationship among our intelligence, memory, and will).

So at one level of analysis there are three distinct persons, but at
another they form a single God.  The East and West differ basically in
how much they emphasize the distinction verses the unity.  In the
East, the analysis starts with the three persons.  Their separate
roles, as shown in the Bible, are described.  They are seen to be a
single God because from a functional point of view acting as God
requires all three.  In the West, the analysis starts with the one
God.  They are seen as distinct only to the extent required to have
the relationship of father to son.  In effect, the Father and Son are
simply two roles that God plays in his relationship with himself.

Ideally, these two models really are simply different ways of looking
at and describing the same thing.  Whether this is true of LDS is
somewhat unclear to me.  From a formal point of view, I'd say your
view is trinitarian if you believe that at the most abstract level of
analysis your three "personages" form a single God.  Because East and
West already differ somewhat in the way they describe things, I
wouldn't necessarily require that your description is identical to any
existing orthodox one.  However in order to qualify as a single God,
I'd say the personages must

  - together constitute a single God
  - function as a single God, i.e. they don't discuss things as
	separate entities and happen to agree -- rather, there
	is only a single action whose formulation and 
	implementation involves them all.
  - exist as intrinsic "parts" of God.  At a minimum this requires
	that they are all eternal.  Obviously if the Son didn't
	come until "later", there was a time when the Father
	was without a Son.  This means that the Son isn't an
	essential part of God.

About "mystery", my answer is also qualified.  My concern is that
people sometimes say this when they simply can't figure out what it
means.  It's probably OK that some Christians don't understand what
the doctrine means.  But if reasonably intelligent people who take the
time to educate themselves can't assign any meaning, there's a
problem.  I do not believe that people fully understand God.  But I do
believe we can understand some things about him.  The trinity is
something we claim we understand to be true.  Thus it's a human
statement.  If the humans who state it don't know what they mean by
it, then I think the doctrine is not very useful.  So I claim that the
doctrine of the trinity may not be complete, but that it had better
say something pretty well-defined.