There is no "I" in "You"

[quip]

Can anyone answer why you're you.....and not me?

Sure.  Different life experiences, for starters.  

By what method of determination do I experience existence separate from your experience; 

We're attached to different sensory systems in separate locations.

more to the point, what determined both our particular experiences

Must be a great many things, assuming anything was determined at all.

and could one have been shunt in place of another (by what alternate means could I have experienced existence through your perspective or vice versa)?
age.

IDK, good questions.  Perhaps whatever we are -is- transferable...might not even need another human to pull the switcharoo with.  

Why here, why now...why not exist a thousand years from now or a thousand years past?

Because your mother and father didn't live a thousand years ago, and won't be alive in a thousand more?

Can this ever be coherently approached or determined materialistically/scientifically? Or, is metaphysics a fundamental necessity?

You;re asking about being, so ofc metaphysics will be necessary, but I doubt that you'll end up with a very accurate statements thereof without reference to the world we live in, or the method by which we generate sound propositions.  More of an "and" than an "or".

You're simply rephrasing the idea.

What determines "my parents";  "my sensory system"...etc in relation to yours prior to either of our extant circumstances?